دوائر كهريائية 2

 ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬ ١١١  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬       W،،‫א‬‫א‬،‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬  ،‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫؛‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬        ،‫א‬ ‫א‬‫א‬   ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،   ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬      ‫א‬  ‫א‬   ،‫א‬     K‫א‬‫א‬،‫א‬‫א‬  ‫א‬  ? ‫א‬ ?  ?  ‫א‬ ? ‫א‬ ‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬   ،‫א‬‫א‬‫א‬ ‫א‬  K‫א‬  ‫א‬‫א‬‫א‬‫א‬         ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬      ،KKK،‫א‬‫א‬‫א‬‫א‬  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬ ‫א‬‫א‬  ‫א‬‫א‬،‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬،‫א‬،‫א‬‫א‬ ،‫א‬‫א‬‫א‬ ‫א‬، ‫א‬،‫א‬‫א‬‫א‬  ‫א‬  K‫א‬‫א‬  KKKKKK،‫א‬     ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ١  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬    ٪١٠٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ‫א‬ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬ K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   -١- K‫א‬‫א‬‫א‬   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Introduction ١J ١ ‫א‬The International system of units ‫א‬‫א‬‫א‬،‫א‬    KElectric Quantities‫א‬‫א‬،‫א‬ ،‫א‬KMetric Prefixes ‫א‬‫א‬‫א‬KScientific Notation ‫א‬‫א‬  KMeasurements Units Conversion‫א‬‫א‬  The International System of Units‫א‬‫א‬‫א‬ ٢J ١    ‫א‬  ‫א‬ ‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ The Measurement Units‫א‬‫א‬ ١J ٢J ١ {  ‫א‬‫א‬  ‫א‬‫א‬‫א‬  W‫א‬‫א‬ ‫א‬  ‫א‬  ‫א‬‫א‬  Basic Quantities Unit‫א‬ Quantity Symbol  m Meter L Length‫א‬  kg Kilogram‫א‬ M Mass‫א‬  A Ampere I Current‫א‬  s Second t  K Kelvin T  cd Candle LI Unit Symbol  Time‫א‬ Temperature‫א‬‫א‬  ‫א‬ Luminous Intensity  The Measurement Units‫א‬‫א‬E١-١F  K‫א‬‫א‬‫א‬Luminous Intensity‫א‬Temperature‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬NForce‫א‬‫א‬{ ‫א‬‫א‬‫א‬ -٢-  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   Watt‫א‬Electric Power‫א‬‫א‬K kg s2  ‫א‬ Nm W s  K Nm  JJoule‫א‬ Electric Energy‫א‬‫א‬K Electric Quantities‫א‬‫א‬  ٢J ٢J ١ ‫א‬‫א‬ ‫א‬Electric Quantities‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  ‫א‬ ‫א‬  ‫א‬ Quantity Unit Quantity Symbol Quantity‫א‬  V Volt V ‫א‬‫א‬  J Joule WE  Electrical Voltage Energy‫א‬  A Ampere I  ‫א‬‫א‬  W Watt‫א‬ P  c Coulomb qQ F Farad‫א‬ C  Electrical Charge Capacitance‫א‬ H Henry L  Inductance‫א‬ Ω Ohm R Resistance‫א‬ Ω Ohm z Impedance‫א‬  Ω Ohm X Reactance‫א‬  Hz Hertz F Frequency‫א‬ Unit Symbol Electrical Current  Power‫א‬ ‫א‬‫א‬  Electric Quantities‫א‬‫א‬E٢-١F -٣-  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬،‫א‬‫א‬‫א‬،Complex Number‫א‬  WK‫א‬  z = R + iX E ١J ١F  Scientific Notation‫א‬‫א‬ ٣J ١ ‫א‬Large and Small numbers‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬KPowers of ten١٠‫א‬   K‫א‬ A * 10 ± n   E٢J ١F  ‫א‬‫א‬، 105 ‫א‬ ‫א‬‫א‬  K‫א‬‫א‬‫א‬K 10 − 5  ‫א‬‫א‬ Power of ten is positive     ‫א‬‫א‬ Power of ten is negative 101 = 10 10 2 = 100 10 3 = 1000  10 5 = 100000    10 −1 = 0.1 10 −2 = 0.01 10 −3 = 0.001 10 −5 = 0.00001  Scientific Notation‫א‬‫א‬E٣J ١F   W 1.5 * 10 6 15 *10 7 150000000Ω ‫א‬ K١  0.3 *10 −6  3 * 10 −7  0.0000003 F  -٤- K٢   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬‫א‬ ٤J ١  The summation‫א‬ •  KE‫א‬F‫א‬‫א‬‫א‬‫א‬  ‫א‬W  E١J ١F  n>m A * 10 n + B * 10 m = A * 10 n − m * 10 m + B * 10 m  = (A * 10 n − m B )* 10 m  The subtraction‫א‬ •  K‫א‬‫א‬‫א‬،   E٢J ١F  n>m  ( ) A * 10 n − B * 10 m = A * 10 n − m − B 10 m The multiplication‫א‬ • WK‫א‬‫א‬ (A * 10 n )* (B * 10 m ) = ( A * B ) * 10 n+ m The division‫א‬ • W K‫א‬J ‫א‬،‫א‬‫א‬ n  (A *10m ) = (B *10 ) A *10 n − m B  E٣J ١F  W‫א‬‫א‬‫א‬‫א‬  a. (2 * 10 6 ) + (5 * 10 7 ) b. (5 * 10 7 ) − (2 * 10 6 ) c. (5 *1012 )* (3 *10 −6 ) d.  (50 * 10 ) (25 * 10 ) -٥- 8 3  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬ (a )(2 *10 6 ) + (5 *10 7 ) = 2 *10 6 + 50 *10 6 = 52 *10 6 (b )(5 * 10 7 ) − (2 * 10 6 ) = (50 * 10 6 ) − (2 * 10 6 ) = 48 * 10 6 (c )(5 *1012 )* (3 *10 −6 ) = (5 * 3) *1012=(−6 ) = 15 *10 6 (d )(50 * 10 3 ) = 50 * 10 8−3 = 2 * 10 5 8 (25 * 10 ) 25 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٥J ١ Power of ten units, prefixes, which attached to the measurement units ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ .Prefixes‫א‬‫א‬‫א‬ {  ‫א‬‫א‬power of ten‫א‬The International System of Units  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ Power of ten ‫א‬ Symbol ‫א‬ Prefixes to the Units  1 * 10−18  a  Atto  f  Femto  1 * 10−12  p Pico  n  Nano  1 *10−6  µ Micro  1 * 10−2  1 * 10−15  1 * 10−9  1 * 10−3  m Milli  c  Centi  1 * 10 −1  d Deci  1 *101  da  Deka  1 * 103  1 *102  h Hecto  k Kilo  1 *106  M Mega  G Giga  1 * 1012  T Tera‫א‬  1 *109  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤J ١F -٦-  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬       E٤J ١F 5kΩ  5 * 10 3 Ω ‫א‬  ٦J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬ {‫א‬ Measurement units Conversion‫א‬‫א‬ ‫א‬KE‫א‬F‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬  W،‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬  E٥J ١F  6Z‫א‬WGiga kilo  9Z‫א‬WPico ‫א‬milli    ‫א‬‫א‬‫א‬، •   W   A * 10 + ( difference) E٣J ١F  E٦J ١F  3Z‫א‬، kΩ ← 5MΩ   ⇒ 5MΩ = 5 *10 3 kΩ ‫א‬‫א‬‫א‬، •   W A * 10 − ( difference) E٤J ١F  E٧J ١F  6Z‫א‬، mF ← 6nF   ⇒ 6nF = 6 * 10 −6 mF  E٨J ١F -٧-  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     µA  0.15mA  A * 10 + ( difference) ⇐   Q micro = 10 −6 Q milli = 10 −3  3Z‫א‬  ⇒ 0,15mA = 0.15 * 10 3 µA = 150 µA  -٨-    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬ Convert the following  K١  (a)4500mV → mV (b)5000nA → mA (c )47000 pF → mF (d )1800 fΩ → mΩ  (e )15mA → A  ( f )0.1ns → s  (g )800µA → mA  :‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٢  29000 kWE  Ω 7000E  0.0003 msE 0.05 AE 0.00009 VE 7000000 VE 0.000000008 sE 9000 kWE  W‫ א‬K٣ µA 800H15mAE  13 msH0.1 nsE 1A+  µA 800E  7000 µA+13 nAE -٩-   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     WA - B، K٤  µA B=800,A=15mAE  B=13 ns A=0.1 msE B= 1000 nA,  µA A=800E  B=7000 µV,A=13mVE  W A ‫א‬، K٥ B  µA B=800,A=15mAE  B=13 ns A=0.1 msE B= 1000 nA,  µA A=800E  B=7000 µV,A=13mVE - ١٠ -  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ٢  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K    ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ‫א‬ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬ K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  - ١١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Introduction١J ٢ ‫א‬{Current‫א‬{Charge‫א‬‫א‬‫א‬‫א‬‫א‬ KPower‫א‬Energy‫א‬‫א‬Electrical Resistance‫א‬‫א‬{Voltage { ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬KAtoms‫א‬‫א‬‫א‬‫א‬ ‫א‬{EH‫א‬FProtons‫א‬{EJ ‫א‬FElectrons‫א‬  KE‫א‬FNeutrons Electrical Charge‫א‬‫א‬ ٢J ٢ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬ ‫א‬‫א‬K  ‫א‬‫א‬‫א‬ ‫א‬‫א‬K e = 1.6 * 10 −19 C ‫א‬‫א‬   K‫א‬ Q = N * e  E١J  N = ±0,1,2,3,.......  ٢F W ‫א‬،‫א‬‫א‬   ‫א‬ ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬   E١J ٢F ‫א‬‫א‬‫א‬K‫א‬  ‫א‬ N = 50 * 1019 ‫א‬‫א‬   K‫א‬  ‫א‬  Q = N * e = 50 * 1019 * 1.6 * 10 −19 = 80.1C - ١٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      K ‫א‬،‫א‬  ‫א‬  W  K   ،?Electrical Field ‫א‬‫?א‬‫א‬‫א‬  W‫א‬K   ‫א‬‫א‬E١J ٢F   {‫א‬‫א‬‫א‬‫א‬‫א‬{ ‫א‬Coulomb‫א‬‫א‬‫א‬‫א‬‫א‬  KC   Electrical Voltage ‫א‬‫ א‬٣J ٢  KV‫א‬‫א‬‫א‬‫א‬‫א‬  Voltage‫א‬ ١J  ٣J ٢ {  ‫א‬‫א‬Work‫א‬‫א‬  W‫א‬Volt - ١٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬ V≡  V=   J C  E٢J ٢F dW  dQ             E٣J ٢F  ‫א‬  V= W Q           E٤J ٢F  W  KV‫א‬WV  KJ‫א‬WW    KCCharge‫א‬WQ  E٢J ٢F ،B‫א‬A‫א‬50C‫א‬600J‫א‬  KBA‫א‬‫א‬  ‫א‬  W،BA‫א‬‫א‬‫א‬‫א‬‫א‬  V= W 600 J = = 12V Q 50C Voltage Sources‫א‬ ٢J ٣J ٢  W،‫א‬‫א‬ Batteries‫• א‬ Solar Cells‫א‬‫• א‬ Electrical Power Supplies‫א‬‫א‬‫א‬‫א‬ • Electrical Generator‫א‬‫א‬‫• א‬ Wind Power Station‫א‬‫א‬‫א‬ • Thermal Stations‫א‬‫א‬‫א‬‫• א‬ Nuclear Stations‫א‬‫א‬‫• א‬ - ١٤ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      Electrical Current ‫א‬‫ א‬٤J ٢ {I‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Current‫א‬١J ٤J ٢ ،E ‫א‬F‫א‬‫א‬  WKCurrent‫א‬‫א‬ I= dQ dt E٥J ٢F  W‫א‬{Ampere‫א‬ A≡ C s E٦J ٢F  W  KA‫א‬:I  KCCharge‫א‬WQ  Kstime‫א‬Wt  Electrons‫א‬{ ‫א‬ ‫א‬‫א‬K ‫א‬‫א‬{  ‫א‬ Free ‫א‬‫א‬Semi–Conductive ‫א‬‫א‬Conductive  K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬Electrons  E٣J ٢F ‫א‬‫א‬WEF‫א‬   ‫א‬‫א‬‫א‬‫א‬F ‫א‬‫א‬‫א‬‫א‬  W،E‫א‬‫א‬‫א‬‫א‬   ‫א‬E٢J ٢F - ١٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬ {‫א‬‫א‬‫א‬  ‫א‬‫א‬{voltage source‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬   K I  E  Load   ‫א‬‫א‬E٣J ٢F     WE٤J ٢F‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬E٤J ٢F  Current Types‫א‬‫א‬٢J ٤J ٢  W‫א‬‫א‬‫א‬ Pure D.C. Current  Current (I)  KE٥J ٢F،‫א‬‫א‬‫א‬‫א‬ time (t)  E٥J ٢F - ١٦ - K١  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Pulsating Current K٢ current ( I )  KE٦J ٢F،‫א‬ time ( t ) current ( I )  time ( t ) current ( I )  time ( t )   Pulsating CurrentE٦J ٢F Alternating Current K٣ sin wave‫א‬‫א‬K‫א‬‫א‬ current ( I )  KAlternating Current‫א‬‫א‬ time ( t )  Alternating CurrentE٧J ٢F - ١٧ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Resistance ‫ א‬٥J ٢ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬ ‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬ K‫א‬‫א‬K‫א‬‫א‬،‫א‬  Resistor‫א‬١J ٥J ٢ ‫א‬،‫א‬‫א‬‫א‬  ،RK‫א‬‫א‬  W‫א‬ R   Resistor‫א‬E٨J ٢F  ‫א‬{ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬Electric Power‫א‬‫א‬{‫א‬‫א‬ Ohm{Ohm‫א‬‫א‬‫א‬{ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬{ Ω  ،‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬{ ‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬ ‫א‬{   ‫א‬‫א‬‫א‬  ‫א‬  W‫א‬ - ١٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬  Current (I)    Resistance (R)  ‫א‬‫א‬‫א‬E٩J ٢F  Resistance of a wire‫א‬‫א‬٢J ٥J ٢  W‫א‬Wires‫א‬  KL{Length‫א‬ K١ KA{Cross-section Area‫א‬ K٢ ‫א‬K{ ρ {MaterialE ‫א‬‫א‬F‫א‬ K٣ K KTTemperature,‫א‬‫א‬ K٤ R= ρ.L A  W‫א‬‫א‬‫א‬ E٧J ٢F  K Ω Resistance‫א‬  W WR  K Ω.m ‫א‬‫א‬ Wρ  K m 2 ‫א‬{Cross-section Area‫א‬ WA  m{Length‫א‬ WL  E٤J ٢F ‫א‬K5m‫א‬،5mm‫א‬‫א‬ 1.72 * 10 −8 Ω m ‫א‬‫א‬، 20o C ‫א‬ - ١٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ R= ρ.L A  W،E٧J ٢F‫א‬R‫א‬ ∴ R = 1.72 ∗ 10 −8 ⎛ ⎞ 5 ⎟ = 4.38 Ω ⎜ ∗ 2 ⎟ ⎜ −3 ⎝ π 5 ∗ 10 2 ⎠ ( )  Types of Resistors‫א‬‫א‬٣J ٥J ٢  W‫א‬  ‫א‬‫א‬‫א‬Opt-photo-ResistorsW‫א‬‫א‬ {‫א‬{‫א‬ K‫א‬‫א‬ { ‫א‬‫א‬‫א‬Thermal-ResistorsW ‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ K١ K٢  ‫א‬‫א‬‫א‬ 10000 1000 ‫أوم‬ 100 10 1 0 40 80 120 160 180 200 ‫درﺟﺔ ﻣﺌﻮﻳﺔ‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٠J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  ‫א‬WVoltage Dependent Resistors‫א‬‫א‬‫א‬ K٣ W‫א‬‫א‬‫א‬‫א‬WLinear Resistors‫א‬‫א‬ K٤ K‫א‬‫א‬‫א‬{VDR - ٢٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     KW‫א‬‫א‬ K ‫א‬‫א‬‫א‬W ‫א‬‫ א‬K  ‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬ W  Potentiometer‫א‬W {Voltage Divider‫א‬ ‫א‬‫א‬{EE،F١١J ٢F٣{٢{١‫א‬  KMega Ohm‫א‬  RheostatW ‫א‬‫א‬‫א‬ ‫א‬{(Kilo OhmF‫א‬ ‫א‬{ ‫א‬‫א‬{‫א‬ ‫א‬‫א‬  ‫א‬‫א‬ 1 KEEF١١J ٢F‫א‬K‫א‬‫א‬‫א‬ 1 + 2 1 2 V13 3 V23 2  EFEF +   -  EF 3 -  ‫א‬‫א‬E١١J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬W ‫א‬‫א‬K K ‫א‬‫א‬{  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٢١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Conductance‫א‬٤J ٥J ٢ ‫א‬‫א‬{‫א‬‫א‬‫א‬ {Ampere per Volt‫א‬‫א‬SiemensG G= R=  W‫א‬ 1 R E٨J ٢F  WKSiemens 1  G E٩J ٢F  K‫א‬‫א‬G‫א‬.Ohm  Energy and Power ‫א‬‫א‬ ٢J ٦  ‫א‬‫א‬١J ٦J ٢ ،Power‫א‬K ‫א‬‫א‬ ‫א‬‫א‬Energy‫א‬ ،KEnergy‫א‬،‫א‬  KEtF‫א‬EWF‫א‬‫א‬Energy‫א‬ P= W t  E١٠J ٢F  W  Kwatt‫א‬Energy‫א‬ P  KJouleWork‫א‬ W  Ksectime‫א‬ t     K‫א‬‫א‬E1 JouleF‫א‬‫א‬‫א‬E1 WattF - ٢٢ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٥J ٢F  ‫؟‬‫א‬‫א‬(5 secF(100 J)‫א‬  P=  ‫א‬ Erergy W 100 j = = = 20W time t 5s   Units of Energy‫א‬‫א‬٢J ٦J ٢ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬Energy‫א‬،‫א‬  Kilo Watt – hour (KWh )‫א‬ K١  Watt – hour (Wh )‫א‬ K٢  Watt – second (Ws )‫א‬ K٣  W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K  KKilo Watt – hour (KWh )‫א‬ KKWh‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K  Watt – hour (Wh )‫א‬ Kilo Watt – hour (KWh )‫א‬ K   K‫א‬‫א‬‫א‬‫א‬  1 E1hF‫א‬‫א‬‫א‬W(1 KWh )  K  WKKW  1KWh = 3.6 MJ .  - ٢٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٦J ٢F 8،250 W‫א‬EKWhF–‫א‬  K  ‫א‬  Energy = W = P.t = (250W ) * (8h ) = (0.25 KW ) * (8h ) = 2 KWh   E٧J ٢F ‫א‬  ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  W‫א‬ (a) 2500w for 2h (b) 100 000w for 5h   W = (2.5 KW ) * (2h ) = 5 KWh W KWh = (100 KW ) * (5h ) = 500 KWh W Joule = (100000W ) * (5 * 3600 s ) = 1800000000 Joule = 18 * 10 8 J = 1.8GJ  W Second ‫א‬Walt ‫א‬‫א‬،Joule ‫א‬ J (KW)‫א‬‫א‬‫א‬ ،KWh‫א‬‫א‬ J  K(hour)‫א‬  - ٢٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Summary‫א‬ {Voltage‫א‬{Current‫א‬{Charge‫א‬‫א‬ ‫א‬‫ א‬K١ KPower‫א‬Energy‫א‬‫א‬Electrical Resistance‫א‬‫א‬  K Q = N * e ،‫א‬‫א‬‫ א‬K٢ {  ‫א‬‫א‬Work‫א‬‫א‬ K٣ KV = dW W ‫א‬Volt dQ ،E ‫א‬F‫א‬‫א‬ K٤ K I = dQ WKCurrent‫א‬‫א‬ dt ‫א‬K‫א‬‫א‬‫א‬‫א‬Energy‫א‬ K٥ K P = W WK‫א‬،Power t - ٢٥ -  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬    ٣  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬     W‫א‬‫א‬  K‫א‬W‫א‬‫א‬  ‫א‬ ،‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬    ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬     W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K - K‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  -٢٦ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬     Introduction١J ٣  ‫א‬‫א‬Fundamental Law‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬{‫א‬‫א‬ George Simon ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬K١٨٢٦Ohm’s LawOhm ‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬ { ‫א‬‫א‬‫א‬‫א‬{  W‫א‬ V R I    Slope = R I +  ‫א‬‫א‬E١J ٣F V −    Ohm’s Law ٢J ٣ ‫א‬Voltage ‫א‬  ‫א‬Current ‫א‬ ‫א‬ ‫א‬  KResistor ‫א‬{‫א‬ ‫א‬‫א‬K ‫א‬   ‫א‬‫א‬    ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬George OhmK‫א‬ ‫א‬K ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬  K‫א‬‫א‬ -٢٧ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬     I A VS +   V R   -   E٢J ٣F   K‫א‬‫א‬‫א‬،    K  ‫א‬‫א‬‫א‬ ‫א‬W  ‫א‬‫א‬ ‫א‬،‫א‬‫א‬  W،‫א‬‫א‬‫א‬  Current Formula‫א‬EF ١J ٣J ٢ ‫א‬، ‫א‬‫א‬ ‫א‬‫א‬  ‫א‬‫א‬‫א‬ E١J ٣F I= VS V , I= R RT  KA‫א‬IW  KVVoltage Source‫א‬ VS   KV{Voltage Drop‫א‬‫א‬V -٢٨ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬     E١J ٣F ،50V‫א‬{100Ω ‫א‬   ‫؟‬‫א‬‫א‬‫א‬  I A  100Ω  V     E١J ٣F‫א‬‫א‬‫א‬E٣J ٣F   ‫א‬  W‫א‬‫א‬ I= V 50 = = 0.5A R 100  W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬R • KI ‫א‬V‫א‬  ‫א‬ ⇐ ‫א‬‫א‬ • K‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ -٢٩ -   ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬    Resistance Formula‫א‬ ١J ٣J ٢  ‫א‬‫א‬K ‫א‬‫א‬‫א‬  ‫א‬  W‫א‬ E٢J ٣F R=  V V , RT = S I IT  W Ω {‫א‬‫א‬‫א‬W R T  KA‫א‬I  K‫א‬‫א‬‫א‬‫א‬ I T  KV‫א‬E  KV‫א‬‫א‬V  E٢J ٣F  ‫؟‬‫א‬{ 75µA ‫א‬{150mV ‫א‬ I = 75µA A   + V    150mV -  E٢J ٣F‫א‬‫א‬‫א‬E٤J ٣F  ‫א‬  W‫א‬ V 150 * 10 −3 R= = = 2 * 10 3 Ω = 2KΩ 6 − I 75 * 10  WNote { ‫א‬‫א‬‫א‬ ‫א‬‫א‬  K‫א‬‫א‬ -٣٠ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬     E٣J ٣F K30V‫א‬‫א‬0.5 mA‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  ‫א‬  W‫א‬ RT = VS 30 = = 60 * 10 3 Ω = 60 kΩ I T 0.5 * 10 −3  E٤J ٣F ‫א‬{10mAR1‫א‬‫א‬‫א‬‫א‬‫א‬  ‫؟‬‫א‬‫א‬،25 V‫א‬ V = 25 V V A R1 I = 10 mA    E٤J ٣F‫א‬‫א‬‫א‬E٥J ٣F R1 =   ‫א‬ V 25 = = 2.5 * 10 3 Ω = 2.5 kΩ − 3 I 10 * 10 Voltage Formula ١J ٣J ٢ K ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K ‫א‬‫א‬‫א‬  W‫א‬‫א‬ -٣١ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬    Voltage Drop‫א‬ ١J ٣J ٢J ٣ ‫א‬{ ‫א‬‫א‬‫א‬‫א‬‫א‬ KE ‫א‬‫א‬F‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬  K‫א‬ E٣J ٣F V = I.R Voltage Source‫א‬ ٢J ٣J ٢J ٣ ‫א‬‫א‬‫א‬‫א‬‫א‬  { R T ‫א‬‫א‬ E٤J ٣F V S = I T .RT  E٥J ٣F ‫א‬‫א‬ 500 Ω ‫א‬ ‫א‬{‫א‬‫א‬  0.1A‫א‬  ‫א‬ V S = I T .RT = 0.1 * 500 = 50 V  E٦J ٣F  3mA‫א‬‫א‬ 27KΩ ‫א‬{‫א‬‫א‬  ‫א‬ V S = I T .RT = 3 * 10 −3 * 27 * 10 3 = 81 V -٣٢ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬     E٧J ٣F  0.8mA‫א‬‫א‬‫א‬، 28 kΩ ‫א‬‫א‬  ‫א‬ V = I * .R = 0.8 *10−3 * 28 *103 = 22.4 V   WNote ‫א‬‫א‬   ‫א‬‫א‬‫א‬{ ‫א‬ ‫א‬‫א‬{‫א‬  W‫א‬‫א‬‫א‬  V  R I     E٦J ٣F   W‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬ V = I*R  R =  I =  V  I      E٥J ٣F         E٦J ٣F V  R           E٧J ٣F  K‫א‬K -٣٣ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬      ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬،‫א‬‫א‬  I A VS  +   V R   ‫א‬‫א‬‫א‬E٧J ٣F    W،‫א‬   ‫א‬‫א‬‫א‬‫א‬E٨J ٣F  E٨J ٣F  W‫א‬،‫א‬‫א‬‫א‬‫א‬   V = 100VandR = 22Ω K  100V   I= R= 22Ω ‫א‬ I 100V = 4,55 A 22Ω  -٣٤ - V = 50V and R = 1kΩ K  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬    I=   ‫א‬ 50V = 50 *10 −3 A = 50mA 1 *10 3 Ω  V = 50kV and R = 100 NΩ K  ‫א‬ 50 * 10 3 I= = 0,5mA 100 *10 6    ‫א‬Ampere   ‫א‬ • Metric Prefixes ‫א‬‫א‬KOhm ‫א‬Volt  K‫א‬‫א‬‫א‬10‫א‬ Ampere‫א‬Volt‫א‬ • Ohm ‫א‬    E٩J ٣F 100Ω 5A‫א‬‫א‬ I =5A  V  R= 100Ω   ‫א‬   I = 5 A, R = 100Ω V = (5 A) * (100Ω ) = 500V  E١٠J ٣F  W‫א‬‫א‬‫א‬،‫א‬‫א‬  -٣٥ - R = 50Ω, I = 5mA K  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬      ‫א‬ V = (5 * 10 −3 A) * (50Ω ) = 250mV   ( ) ( R = 3.3kΩ, I = 10mA K  ‫א‬ ) V = 10 * 10 −3 A * 3,3 * 10 3 Ω = 33V   E١١J ٣F 3A‫א‬‫א‬12V‫א‬‫א‬  3A    R 12V   ‫א‬  R= 12V = 4Ω 3A  V = 12V , I = 3 A  E١٢–٣F  W‫א‬‫א‬،‫א‬‫א‬  I = 68,2µA and  V = 150v  ‫א‬   R = 150v = 2.2MΩ 68,2µA -٣٦ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬     Summary‫א‬  K‫א‬‫א‬‫א‬‫א‬ K١ { ‫א‬{ ‫א‬  ، ‫א‬Current‫א‬ K٢ KI = V W R W{‫א‬‫א‬‫א‬ K٣ V = I*R ‫א‬‫א‬‫א‬ I T ‫א‬‫א‬‫א‬‫א‬ K٤ K‫א‬‫א‬، R T ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬ K٥ K‫א‬‫א‬‫א‬ -٣٧ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬    ‫א‬‫א‬     ‫א‬‫א‬‫א‬‫א‬ K١ W  K‫א‬ K١ K75%‫א‬ K٢ K‫א‬ K٣ K35%‫א‬ K٤ K‫א‬‫א‬‫א‬‫א‬ K٥  K‫א‬‫א‬‫א‬‫א‬ K٦  W‫א‬{‫א‬‫א‬ K٢  V = 5V , R = 1Ω K١ V = 15V , R = 10Ω K٢  V = 50V , R = 100Ω K٣  V = 30V , R = 15KΩ K٤  V = 250V , R = 5.6MΩ K٥ ‫؟‬‫א‬‫א‬‫א‬{12V10KΩ  K٣ {  J J J W ‫א‬‫א‬‫א‬ K٤ K12V‫א‬‫א‬‫א‬‫א‬{ ‫א‬‫א‬‫א‬‫א‬{25V K٥ KJ J J W‫א‬‫א‬‫א‬   -٣٨ -  ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٦  ‫א‬‫א‬‫א‬  8Ω ‫א‬‫א‬ ، W‫א‬  Fuse R 120V V 100V    { ‫א‬‫א‬‫א‬Fuse‫א‬  ‫؟‬100 V‫א‬‫א‬‫א‬  W‫א‬‫א‬R‫א‬I‫א‬‫א‬‫ א‬K٧  I = 2A ,  I = 2.5A , I = 5A , R = 18Ω EF R = 680Ω EF R = 56Ω EF  ‫א‬{3A 27Ω ‫א‬‫א‬ K٨ ‫؟‬‫א‬K W‫א‬‫א‬I‫א‬{V‫א‬‫א‬‫ א‬K٩  I = 2A ,  I = 45A ,  I = 5A , -٣٩ - V = 10V EF V = 90V EF V = 50V EF   ‫א‬‫א‬  ١١١  ‫א‬    ‫א‬  ‫א‬      R = 100Ω ‫א‬{ ‫א‬‫א‬‫א‬‫א‬ K١٠ ‫א‬‫א‬‫א‬{‫א‬Variable Voltage Source ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K100 V‫א‬‫א‬ ‫א‬‫א‬KI‫א‬V‫א‬‫א‬‫א‬K  ‫؟‬‫א‬‫א‬‫א‬‫؟‬ K V = 1V   ‫א‬ I = 5mA ‫א‬‫א‬ K١١ W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  V = 1.5V EF EF V = 2V EF  V = 3V  V = 4V EF  V = 10V EF K‫א‬‫א‬{I‫א‬V‫א‬{‫א‬‫א‬ { ‫א‬‫א‬‫א‬‫א‬{  ‫א‬‫א‬ K١٢ K R = 3.3kΩ R = 3.9kΩ 75V 50V R = 4.7 kΩ 100V -٤٠ -      ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ٤  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬   K‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬     W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬   - ٤٢ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction ١J ٤ ‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬       K‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬   KPower‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬Energy‫א‬‫א‬‫א‬‫א‬  Power ‫ א‬٢J ٤ KWatt‫א‬ Watt‫א‬‫א‬K ‫א‬‫א‬‫א‬ t‫א‬‫א‬KP  W‫א‬‫א‬ E١J ٤F Power = E٢J ٤F Energy time P= E t  ‫א‬L‫א‬Z‫א‬  KWatt‫א‬Power‫א‬  K Watt ‫א‬‫א‬JEnergy‫א‬ sec ond  Ksecondtime‫א‬  W  W WP WE Wt   WNote WattW{ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬K‫א‬Joule‫א‬ E٣J ٤F Watt = - ٤٣ - Joule sec ond  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١J ٤F  ‫؟‬‫א‬‫א‬{5 sec‫א‬100 J‫א‬‫א‬  ‫א‬ Power = Energy E 100 J = = = 20 Watt time t 5 sec  W‫א‬  E٢J ٤F  ‫؟‬‫א‬Kt = 30 sec‫א‬‫א‬‫א‬{P = 100 W‫א‬‫א‬  ‫א‬ Power = Energy ⇒ Energy = Power * time time E = P * t = 100 * 30 = 3000J = 3 kJ  WNote  KWEEnergy‫א‬‫א‬  E٣J ٤F  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  0.045 W EF 0.000012 W E F 3500 W E F  10, 000, 000 W E F  ‫א‬ ‫א‬‫א‬‫א‬KMWkWWmW‫א‬‫א‬ ‫א‬‫א‬،mW‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬KKW‫א‬‫א‬‫א‬‫א‬‫א‬  WKMW‫א‬‫א‬‫א‬ - ٤٤ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    mW‫א‬‫א‬‫א‬،‫א‬،P=0.045 W EF  W P = 0.045 W = 0.045 * 10 3 * 10 −3 W = 45 * 10 −3 = 45 mW ‫א‬،‫א‬‫א‬،P=0.000012 W E F ‫א‬، µW ‫א‬‫א‬‫א‬‫א‬،‫א‬ W P = 0.000012 W = 0.000012 * 10 6 * 10 −6 W = 12 µW W‫א‬kW،P=3500 W EF P = 3500 W = 3500 * 10 −3 * 10 3 W = 3.5 kW WMW‫א‬،P=10,000,000 W EF P = 10,000,000 W = 10,000,000 * 10 −6 * 10 6 W = 10 MW  WNote W‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J  E٤J ٤F W‫א‬‫א‬‫א‬‫א‬  KE‫א‬F1400 WEF  KEF2500 WEF  KEF1,000,000 WEF - ٤٥ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  a. 1400 W = 1400 10 3 = 1.4 kW W = P * t = 1.4 kW * 1h = 1.4 kWh 2500 W = 2500 10 3 = 2.5 kW b. W = P * t = 2.5 kW * 2h = 5 kWh 1000000 W = 1000000 10 3 = 1000 kW c. W = P * t = 1000 kW * 5h = 5000 kWh Power in Electric Circuit‫א‬‫א‬‫א‬‫א‬ ٣J ٤ ‫א‬،‫א‬‫א‬Power‫א‬ ‫א‬،‫א‬،‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ KOhm’s Law‫א‬‫א‬‫א‬‫א‬‫א‬ E٤J ٤F  W‫א‬‫א‬‫א‬ P = V.I  W  KWatt‫א‬{Power‫א‬ WP  KV{‫א‬ WV  KA‫א‬ - ٤٦ - WI  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     I  +   R V    ‫א‬E١J ٤F  ‫א‬ V = I.R ‫א‬‫א‬‫א‬   W‫א‬ E٥J ٤F ‫א‬ I = P = V.I = I.R.I = I 2 .R V ‫א‬، R  W‫א‬ V V2 P = V.I = V. = R R V E R = , RT = I IT E٦J ٤F E٧J ٤F E٥J ٤F  W‫א‬‫א‬{10Ω ‫א‬‫א‬ I=0.7AEF  I=1.4AEF  I=2.1AEF - ٤٧ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  W‫א‬‫א‬ a. P = I 2 .R = (0.7) 2 * 10 = 4.9W b. P = I 2 .R = (1.4) 2 *10 = 19.6W P = I 2 .R = (2.1) 2 *10 = 44.1W c. IP‫א‬‫א‬‫א‬،‫א‬‫א‬ E٨–٤F           WK  P α I 2  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ P = 4.9 Watt ← I = 0.7 A EF  P = 16.6Watt ← I = 1.4A EF  KEF‫א‬EF‫א‬EF   E٦J ٤F ‫א‬،15 V10 kΩ ‫א‬‫א‬{‫א‬‫א‬  K‫א‬12 kΩ ‫א‬ 12 kΩ +  V  I -  15V 10kΩ  −  E٦J ٤F‫א‬‫א‬‫א‬E٢J ٤F - ٤٨ -  +  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  ‫א‬‫א‬‫א‬‫א‬ I= V 15 15 = = 4 = 1.5 mA 3 R 10 * 10 10 V = I*R = 1.5 * 10 −3 * 12 * 10 3 = 18 V  KV=18 V ‫א‬   E٧J ٤F  ‫؟‬‫א‬‫א‬‫א‬120v100w  ‫א‬  Q P = V .I ⇒ I =  ∴I = p v 100w = 0.83 A 120v  E٨–٤F  2A  R 10V W‫א‬‫א‬‫א‬‫א‬‫א‬ I 2A 50Ω V  10Ω 5V   (b ) (a) (c)  ‫א‬  (a )l = VI = (10V ) * (2 A) = 20w  (b )L = I 2 * R = (2 A 2 )* (50Ω ) = 200W   ( ) 2 2 (c )L = V = 5v 25 = 2,5W R 10Ω 10   - ٤٩ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Power Rating of Resistors‫א‬‫ א‬٤J ٤  Definition١J ٤J ٤ ‫א‬  ‫א‬‫א‬Power Rating of Resistors‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬،EF،   W WPower Rating‫א‬‫א‬‫• א‬ 1 1 1 W , W , W ,1W , and 2W 2 4 8 ‫א‬‫א‬‫א‬ ‫א‬‫• א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬،Surface Area K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٤J ٤  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،The Power RatingE‫א‬‫א‬‫א‬‫א‬F‫א‬E‫א‬F  K‫א‬‫א‬‫א‬EF‫א‬‫א‬   E٩–٤F  K‫א‬‫א‬،10v‫א‬ 62Ω   ‫א‬   QV = 10VandR = 62Ω  W‫א‬‫א‬‫א‬‫א‬‫א‬ P= v 2 100 = = 1.6w R 62  K 2W ‫א‬  K‫א‬‫א‬E1wF1.6w‫א‬‫א‬‫א‬   - ٥٠ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Resistor Failures‫א‬EF٣J ٤J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K ‫א‬‫א‬‫א‬،Power Rating  KOhmmeter ‫א‬‫א‬‫א‬‫א‬،‫א‬  - ٥١ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Summary‫א‬ K Watt = Joule W،‫א‬‫א‬‫א‬‫• א‬ sec ond K‫א‬ • ‫א‬‫א‬‫א‬‫• א‬ K‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫• א‬ Kopen circuit‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫• א‬ K KAmpere. Hourx‫א‬ • K١١x‫א‬‫• א‬         - ٥٢ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬  ‫؟‬ 350 j s ‫א‬‫א‬‫א‬ K١  ‫؟‬ 5h  7500 j ‫א‬‫א‬ K٢  ‫ ؟‬50ms 1000 j ‫א‬‫א‬‫א‬ K٣   3750w EF  kw ‫א‬‫א‬‫א‬ K٤   1000w EF  500 w EF  50000 w EF   Kx‫א‬Ex‫א‬ 5 *106 F‫א‬ K٥ ‫א‬ 2A  75V ‫א‬‫א‬‫א‬ K٦  ‫؟‬ R L ‫א‬ ‫א‬‫א‬ 3A ‫א‬120V  K٧  ‫؟‬‫א‬  ‫؟‬100µA 10kΩ ‫א‬‫א‬‫ א‬K٨  - ٥٣ -   ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ٥  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٣ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬   - ٥٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction ١J ٥ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Conductor ‫א‬،Capacitor‫א‬،Resistor ‫א‬K ‫א‬ K ‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬ ،  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Series Connection‫א‬‫א‬ K١ Parallel Connection‫א‬‫א‬ K٢ Series-Parallel Connection‫א‬‫א‬ K٣ ‫א‬ ‫א‬‫א‬  ،  ‫א‬‫א‬‫א‬‫א‬    ‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ ‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٢J ٥  Series Circuit‫א‬‫א‬‫א‬ Series Connection‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬ ‫א‬ K  ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ K‫א‬KKKKKKKKK‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬، - ٥٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     R1 R1 R1 a a R2 R3 R3 b  a R2 R2 I  R3  b R4 b  I I  ‫א‬‫א‬‫א‬ E١J ٥F Total Resistance (RT)‫א‬‫ א‬١J ٢J ٥  RT  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ = R1 + R2 + R3 + K + Rn E١J ٥F   E١J ٥F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬ R 1 = 56 Ω R 2 = 100 Ω   I R3 = 27 Ω VS R 5 = 5.6 Ω R 4 = 10 Ω  E١J ٥F‫א‬‫א‬‫א‬E٢J ٥F - ٥٦ -      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ RT = 56Ω + 100Ω + 27Ω + 10Ω + 5.6Ω = 198.6Ω ∴ R T = 198.6Ω  E٢J ٥F ‫א‬‫א‬‫א‬K  ‫א‬‫א‬   ‫א‬‫א‬  K 22 Ω  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Q R T = nR            E٢J ٥F  ∴ R T = 8 * 22 = 176 Ω  K‫א‬ n W Ohm's Law in Series Circuits ‫א‬‫א‬‫א‬ ٣J ٥ ،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬  E٣J ٥F ،12.6 kΩ ‫א‬‫א‬‫א‬ ‫א‬‫א‬  W‫א‬‫א‬‫א‬ 3.9 kΩ ‫א‬Voltage Drop‫א‬ R1  R2 R3 =3.9 kΩ Vs = 20 V  + V=? _  E٣J ٥F‫א‬‫א‬‫א‬E٣J ٥F - ٥٧ -      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ I‫א‬ ،‫א‬ R2،R1‫א‬  ‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ I= VS 20 = = 1.59mA R T 12.6 * 103 V3 = I * R3 = 1.59 * 10 −3 * 3.9 * 10 3 = 6.19V  6.19 VR3‫א‬‫א‬∴   E٤J ٥F KVs،‫א‬‫א‬‫א‬  K 5mA Fuse‫א‬ Vs‫א‬ 5 mA Fuse + VS R 1 = 1 kΩ R 2 = 3.3 kΩ I = 1mA − R 3 = 4.7 kΩ   E٤J ٥F‫א‬‫א‬‫א‬E٤J ٥F   ‫א‬  W‫א‬‫א‬ V1 = IR 1 = (1mA ) ⋅ (1KΩ ) = 1 * 10 −3 * 10 3 = 1V ( ) = (1mA ) ⋅ (4.7 * 10 Ω ) = 1 * 10 V2 = IR 2 = (1mA ) ⋅ 3.3 * 10 3 = 3.3V V3 = IR 3 3 3 * 4.7 * 10 3 = 4.7 V  KRTVS‫א‬ ∴ R T = 1 + 3.3 + 4.7 = 9KΩ VS = 1 * 10 −3 * 9 * 10 3 = 9V - ٥٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     WVSV1،V2 ،V3  VS = V1 + V2 + V3 = 9V EKirchhoff’s Voltage LawF‫א‬ ‫א‬  VS‫א‬EF‫א‬  K‫א‬‫א‬‫א‬   WNote  K‫א‬‫א‬‫א‬EKVLF  5mA‫א‬‫א‬  W‫א‬ VS = 5mA * 9KΩ VS = 5 * 10 −3 * 9 * 10 3 = 45V  E٥J ٥F  ‫؟‬VS‫א‬،1mA ‫א‬‫א‬‫א‬‫א‬‫א‬  − VS +    1.5 kΩ 1.2 kΩ I 1.2 kΩ   5.6 kΩ  E٥J ٥F‫א‬‫א‬‫א‬E٥J ٥F - ٥٩ -    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ RT‫א‬‫א‬،VS‫א‬ R T = 1.2 + 5.6 + 1.2 + 1.5 = 9.5kΩ ∴ R T = 9.5kΩ  VS‫א‬ VS = IR T = (1mA ) ⋅ (9.5kΩ ) = 1 * 10 −3 * 9.5 * 10 3  ∴ VS = 9.5V  Voltage Sources in Series‫א‬‫א‬‫א‬ ٤J ٥ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K  ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬  E٦J ٥F ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ E2،E1‫א‬W‫א‬‫א‬‫א‬  KRT‫א‬   + 30 V +− 20 V −  V S1 R T = 200 Ω VS 2      E٦J ٥F‫א‬‫א‬‫א‬E٦J ٥F - ٦٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ ‫א‬‫א‬،‫א‬‫א‬ E1،E2‫א‬  W‫א‬ V ST = V S1 + V S 2 V ST = 30 + 20 = 50V  W ∴I = V ST 50 = = 0.25 A RT 200 ∴ I = 0.25A ‫א‬‫א‬،ESeries–OpposingF‫א‬‫א‬ ‫א‬‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬  KE٧J ٥F‫א‬   E٧J ٥F  W‫א‬‫א‬‫א‬‫א‬ + 25V − + 15V −   V RT S1   VS2     E٧J ٥F‫א‬‫א‬‫א‬E٧J ٥F - ٦١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ ‫א‬‫א‬‫א‬ VS1 , VS ‫א‬ 2 ‫א‬–H‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬ V ST = V S 2 − V S 2 V ST = 25 − 15 = 10 V  E٨J ٥F ‫א‬،‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫؟‬‫א‬‫א‬ − E1 + 1.5V − E 2 + − E3 + − E 4 + 1.5V 1.5V 1.5V ET  E٨J ٥F‫א‬‫א‬‫א‬E٨J ٥F  ‫א‬ V ST = 4 * 1.5 = 6 V  E Kirchhoff's voltage law (KVL ٥J ٥ ‫א‬‫א‬‫א‬  ‫א‬‫א‬  K?‫א‬EF‫א‬‫א‬‫?א‬  W Voltage Drops‫א‬‫א‬‫א‬ ‫א‬‫א‬Voltage Drops‫א‬‫א‬  K  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ - ٦٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    K  ‫א‬‫א‬ ‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R1 R2 R3 − V1 + − V2 + − V3 +  R4 − V4 +      VS  ‫א‬‫א‬‫א‬‫א‬‫א‬E٩J ٥F  W،‫א‬‫א‬ v s = v1 + v 2 + v 3 + v 4 ‫א‬Voltage Drops‫א‬  W،‫א‬ v s = v1 + v 2 + v 3 + ..........   E٩J ٥F  W‫א‬‫א‬‫א‬،‫א‬‫א‬ VS ‫א‬  + VS + 5V - − + 10V −  E٩J ٥F‫א‬‫א‬‫א‬E١٠J ٥F - ٦٣ -       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  K v s = v1 + v 2 v s = 5 + 10 = 15v ∴ v s = 15v  E١٠J ٥F ‫א‬، I = 200mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  ‫؟‬ R 4  R 3 ، R 2 ، R1 ‫א‬   R 3 = 100 Ω R 2 = 47 Ω  R1 = 10 Ω R4     E=100 V  I = 200 mA  E١٠J ٥F‫א‬‫א‬‫א‬E١١J ٥F   ‫א‬  ‫א‬‫א‬ Ohm’s Law  K Kirchhoff's Voltage Law  Voltage Drops‫א‬‫א‬‫א‬W  V1 = IR 1 = 200 * 10 −3 * 10 = 2V V2 = IR 2 = 200 * 10 −3 * 47 = 9.4V V3 = IR 3 = 200 * 10 −3 * 100 = 20V - ٦٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     WE R 4 ‫א‬‫א‬F v 4  v s − (v 1 + v 2 + v 3 + v 4 ) = 0 100 − 2 − 9.4 − 20 − v 4 = 0 68.6 − v 4 = 0 ∴ v 4 = 68.6V Voltage Divider ‫א‬ ٦J ٥ Voltage Divider Law‫א‬١J ٦J ٥ ‫א‬‫א‬‫א‬  ‫א‬‫א‬  KE‫א‬F‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Voltage Dividers‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  − V1 + R1 + VS  I R2 −  + V2   _   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ٥F  ‫א‬‫א‬ R 2 ، R1 ‫א‬‫א‬  W‫א‬ V1 = IR 1 V2 = IR 2  K R1, R 2  V2 ، V1 ‫א‬‫א‬  W R 2 = 100Ω ، R1 = 50Ω ، VS = 10V ‫א‬، - ٦٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   R T = 50 + 100 = 150Ω I=  10 V 1 = A 150 Ω 15 V1 = IR 1 = ∴ V1 = 1 1 * 50 = * 10 V 15 3 1 (10) V 3 V2 = IR 2 = ∴ V2 = 1 1 * 100 = (20) V 15 3 2 (10) V 3 ‫א‬K ‫א‬ V2 ‫א‬ V1 ‫א‬  K‫א‬‫א‬‫א‬‫א‬ ٢-٦-٥ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Voltage Divider Formula ‫اﻟﺼﻴﻐﺔ اﻟﻌﺎﻣﺔ ﻟﺘﻮزﻳﻊ اﻟﺠﻬﺪ‬  W‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ R1 V1 + − R3 R2 V2 + − V3 + −  R4  V4 + − I     VS + −  ‫א‬E١٣J ٥F - ٦٦ -    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W،‫א‬ X  VX ‫א‬‫א‬ VX = IR X           E٣–٥F   4 ، 3، 2،1‫א‬ x W    W‫א‬‫א‬‫א‬  I = VS  RT    E٤–٥F  E٣J ٥F‫א‬ I ‫א‬ ⎛ VS ⎞ ⎟⎟R X  R ⎝ T⎠  VX = ⎜⎜ E٥J ٥F  W VX ‫א‬ ⎛R ⎞ VX = ⎜⎜ X ⎟⎟VS  ⎝ RT ⎠  E٦J ٥F   E١١J ٥F  ‫؟‬‫א‬‫א‬‫א‬ V2 ‫א‬ V1 ‫א‬   R 1 = 100Ω + VS = 10 V + V1 − − R 2 = 56 Ω + V2 −  E١١J ٥F‫א‬‫א‬‫א‬E١٥J ٥F - ٦٧ -         ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  E٦J ٥F‫א‬ V2 ، V1  ⎛R ⎞ VX = ⎜⎜ X ⎟⎟VS ⎝ RT ⎠   R T ‫א‬‫א‬ R T = 100 + 56 = 156Ω ⎛R ⎞ 100 V1 = ⎜⎜ 1 ⎟⎟VS = * 10 = 6.41V 156 ⎝ RT ⎠ ∴ V1 = 6.41V  W، V2  ⎛R V2 = ⎜⎜ 2 ⎝ RT ⎞ 56 ⎟⎟VS = *10 = 3.59V 156 ⎠  W، V2 ،‫א‬‫א‬ V2 = VS − V1 = 10 − 6.41 = 3.59V   E١٢J ٥F  E١٥J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬  C to D (e) B to D (d) B to C (c) A to C (b) A to B (a)  W‫א‬  VCD (e) VBD (d) VBC (c) VAC (b) VAB (a) - ٦٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   A  R1 = 1kΩ   B   VS = 25V R2 = 8.2kΩ  C   R3 = 3.3kΩ  D   E١٢J ٥F‫א‬‫א‬‫א‬E١٥J ٥F  ‫א‬  R T ‫א‬‫א‬ R T = R1 + R 2 + R 3 RT = 1 + 8.2 + 3.3 = 12.5kΩ  W‫א‬،‫א‬‫א‬‫א‬  WA,B‫א‬‫א‬ • ⎛R ⎞ VAB = ⎜⎜ 1 ⎟⎟VS ⎝ RT ⎠ VAB = 1 * 25 = 2V 12.5 ∴ VAB = 2V  A,C‫א‬‫א‬ •  ⎛ R + R2 ⎞ ⎟⎟VS V AC = ⎜⎜ 1 ⎝ R3 ⎠ 9.2 ⎞  VAC = ⎛⎜ ⎟ * 25 = 18.4V ⎝ 12.5 ⎠ ∴ VAC = 18.4V - ٦٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     B،C‫א‬‫א‬ • ⎛R VBC = ⎜⎜ 2 ⎝ RT ⎞ ⎟⎟VS ⎠ ⎛ 8.2 ⎞ VBC = ⎜ ⎟ * 25 = 16.4V ⎝ 12.5 ⎠  ∴ VBC = 16.4V  B،D‫א‬‫א‬ • 8.2 + 3.3 ⎞  VBD = ⎛⎜ ⎟ * 25 ⎝ 12.5 ⎠ ⎛ 11.5 ⎞ VBD = ⎜ ⎟ * 25 = 23V ⎝ 12.5 ⎠ ∴ VBD = 23V  VCD ‫א‬ • ⎛ 3.3 ⎞ VCD = ⎜ ⎟ * 25 = 6.6 ⎝ 12.5 ⎠ ∴ VCD = 6.6V    ‫א‬‫א‬ { ‫א‬‫א‬ ‫א‬K   ‫א‬‫א‬‫א‬‫א‬  K‫א‬   - ٧٠ -   E١٣J ٥F V3 ,V2 ,V1 EF C, A ‫א‬‫א‬‫א‬EF  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     D, B ‫א‬‫א‬EF   A 1kΩ V1 R1  B Vs R2 R3 3.3kΩ C    V2 10kΩ    V3 D   E١٣J ٥F‫א‬‫א‬‫א‬E١٦J ٥F    ‫א‬  RT = R1 + R2 + R3 = 14.3hΩ (1)V1 = R1 1hΩ = Vs = * 25V = 1,75V 14.3hΩ RT R1 = Vs = 17,5V RT R V3 = 3 Vs = 5,75V (or : V3 = Vs − V1 − V2 ) RT R + R2 11hΩ (2)V AC = 1 * Vs = * 25V = 19.25V RT 14,3hΩ R +R  (3)V BD = 2 3 * Vs = 23.25V RT V2 =  - ٧١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      W‫א‬‫א‬Potentiometer‫א‬‫א‬   1 3 Vs 2   R13 Vs  R23   ‫א‬‫א‬‫א‬‫א‬‫א‬EJ ١٧J ٥F  Power in a Series Circuit ‫א‬‫א‬‫א‬‫ א‬٧J ٥ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬   W PT = P1 + P2 + ........... + Pn E٧J ٥F  K‫א‬‫א‬‫א‬ PT    1)   2) PT = VS I   W‫א‬‫א‬‫א‬‫א‬‫א‬   PT = I 2 RT  V S2  3) PT = RT      E٨J ٥F      E٩J ٥F  E١٠J ٥F  - ٧٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١٣J ٥F  W‫א‬‫א‬‫א‬‫א‬‫א‬ R1 = 10 Ω R2 = 18 Ω R3 = 56 Ω VS = 15 V R4 = 22 Ω  E١٣J ٥F‫א‬‫א‬‫א‬EJ ١٧J ٥F  ‫א‬  K‫א‬‫א‬ R T = 10 + 18 + 56 + 22 = 106 Ω  W‫א‬E١٠J ٥F‫א‬‫א‬‫א‬‫א‬ VS2 (15)2 ∴ PT = = = 2.12 W RT 106  EJ ١٤J ٥F  ،0.5 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫؟‬‫א‬‫א‬‫א‬ R1 = 1kΩ  R2 = 2.7kΩ  R3 = 910Ω VS = 120 V R4 = 3.3kΩ  EJ ١٤J ٥F‫א‬‫א‬‫א‬EJ ١٨J ٥F - ٧٣ -       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  ‫א‬‫א‬ R T = R1 + R 2 + R 3 + R 4 R T = 1 + 2.7 + 0.91 + 3.3 = 7.91 kΩ R T = 7.91 kΩ I= VS 120 = = 15.2 mA R T 7.91  ‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬ P1 = I 2 R 1 = (15.2 mA )2 (1 kΩ ) = 231 mW P2 = I 2 R 2 = (15.2 mA )2 (2.7 kΩ ) = 624 mW = 0.62 W P3 = I 2 R 3 = (15.2 mA )2 (910 Ω ) = 210 mW = 0.21 W  P4 = I 2 R 4 = (15.2 mA )2 (3.3 kΩ ) = 762 mW = 762 = 0.762 W 1000    ‫א‬‫א‬ ‫א‬‫א‬ R 4 ، R 2   W‫א‬‫א‬،15.2mW P2 = 0.62 W > 1 W 2 P4 = 0.762 W > 1 W 2  K‫א‬1w‫א‬‫א‬‫א‬  - ٧٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     EJ ١٤J ٥F  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  R1= 10Ω I  R2= 100Ω Vs=15V    R3=1k  E١٤J ٥F‫א‬‫א‬‫א‬EJ ١٨J ٥F   RT    ‫א‬ RT W‫א‬‫א‬‫א‬‫א‬  = R1 + R2 + R3 ⇒ RT = 110Ω  W PT ‫א‬ 2 V PT = s = 0.2W  RT  W  ، ‫א‬‫א‬‫א‬  P1 + P2 + P3  ‫א‬   K‫א‬‫א‬  W،I‫א‬‫א‬  I= Vs 15v = = 13,5mA RT 1110Ω  W،‫א‬      P1 = I 2 * R1 = 1.8mW P2 = I 2 * R2 = 18mW P3 = I 2 * R3 = 180mW  W‫א‬‫א‬‫א‬، PT = P1 + P2 + P3 = 0.2W - ٧٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Voltage With Respect to Ground ‫א‬ ٨J ٥ E‫א‬F ‫א‬‫א‬  ‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬،Reference Point. ‫א‬،100V‫א‬‫א‬‫א‬  KCircuit Ground‫א‬‫א‬‫א‬100V‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ ،‫א‬Ground‫א‬ ‫א‬‫א‬  KE١٩J ٥F   + R1 +  V1  − V2  a −  + R2 V2  V  −  Ground‫א‬E١٩J ٥F     Ka‫א‬ ‫א‬ - ٧٦ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١٥J ٥F ،‫א‬‫א‬‫א‬‫א‬‫א‬  K25 VVoltage Dropped ‫א‬‫א‬ + − + + − c a b + a + b + + −   −  c  +  100V 100V − − + e − + d e d  − − −  (a)  (b)  + − a C c b + + 100V − − e + − d (c)   E١٥J ٥F‫א‬‫א‬‫(א‬a-b-c)E٢٠J ٥F  ‫א‬  W‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬EaF‫א‬‫א‬  Va ‫א‬،a‫א‬‫א‬، Va ‫א‬  K‫א‬a‫א‬‫א‬a‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬EaF‫א‬‫א‬ Ve = 0 - ٧٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   Vd = +25V  Vc = +50V Vb = +75V Va = +100V  W‫א‬‫א‬d‫א‬Eb F‫א‬‫א‬ Ve = −25V Vd = 0V  Vc = +25V Vb = +50  Va = +75V  W‫א‬‫א‬،c‫א‬،EcF‫א‬‫א‬ Ve = −50V Vd = −25V Vc = 0V Vb = +25V Va = +50V ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬ ‫א‬،a‫א‬‫א‬‫א‬  K‫א‬  W‫א‬‫א‬  Ke ← ،d،c،b‫א‬  ‫א‬a‫א‬‫א‬‫א‬ KJ ،H‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  W VA EaF‫א‬‫א‬ Va = VS = 100V Vb = 100 − 25 = +75V Vc = 100 − 25 − 25 = +50V - ٧٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   Vd = 100 − 25 − 25 − 25 = +25V   ‫א‬e‫א‬ Ve = Vs + Vb + Vc + Vd + Ve Ve = 100 − 25 − 25 − 25 − 25 = 0 ∴ Ve = 0  WNote    W‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬W  ‫א‬‫ א‬E١ ‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬   KE‫א‬‫א‬F‫א‬‫א‬ ‫א‬‫א‬‫א‬W ‫א‬‫ א‬E٢ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  W R1 ‫א‬ Vb = Vs − IR 1  Kc،b،a‫א‬‫א‬‫א‬‫א‬ Troubleshooting ‫א‬‫א‬ ٩J ٥  W‫א‬‫א‬،‫א‬‫א‬‫א‬  KOpen Circuit ‫א‬‫א‬‫א‬‫א‬‫א‬ E١F KShort Circuit‫א‬‫א‬‫א‬‫א‬‫א‬ E٢F ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬    ‫א‬‫א‬‫א‬    ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،Open Circuit‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬ ‫א‬‫א‬‫א‬ K١   - ٧٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    V = IR = 0 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬ Cheek For Burned Resistor‫א‬‫א‬ K٢ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 0V R1 + 10V − 0V R2 R2 VS = 10V Open Circuit‫א‬‫א‬E٢١J ٥F          ‫א‬‫א‬KShort‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬  K‫א‬‫א‬‫א‬‫א‬  - ٨٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١٦J ٥F K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬، VS = 100V   K‫א‬‫א‬‫א‬‫א‬‫א‬E  ‫؟‬‫א‬‫؟‬‫א‬،‫א‬‫א‬ a, b ‫א‬Short‫א‬E 10Ω  18Ω c b − VS = 100V 33Ω + 39Ω  a       E١٦J ٥F‫א‬‫א‬‫א‬E٢٢J ٥F  ‫א‬  K R T ‫א‬W  R T = 10 + 18 + 33 + 39 = 100 Ω I= 100 =1A 100 ‫א‬‫א‬‫א‬‫א‬a , b‫א‬ShortW   E٢٣–٥FK‫א‬‫א‬‫א‬ A, B   ‫א‬‫א‬‫א‬ R T = 18 + 10 = 28 Ω - ٨١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    10Ω  18Ω b C − VS = 100V   33Ω I +    a  E١٦J ٥F‫א‬‫א‬‫א‬E٢٣J ٥F I= VS 100 = = 3.57 A RT 28   39Ω     W‫א‬  K 3.57 A   1 A ‫א‬‫א‬، A, B ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬  A, C ،‫א‬‫א‬‫א‬ ‫א‬‫א‬18 Ω ، 33 Ω ، 39 Ω ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ R T = 10 Ω I= VS 100 = = 10 A R T 10  K10 A ‫א‬‫א‬ - ٨٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Summary ‫א‬ K‫א‬‫א‬‫א‬‫א‬‫ א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ KKVL‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ Series-Opposition‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬Voltage Drops‫א‬ ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬Ground‫א‬ K‫א‬Negative Ground‫א‬‫ א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬Positive Ground‫א‬‫ א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬Open circuit‫א‬‫א‬‫א‬‫ א‬  K‫א‬ - ٨٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬ K A, B ‫א‬‫א‬‫א‬‫א‬‫א‬ K١ R1 A A B    R2 R1 R2  R3 R3  B    A R2 R1 B R4 R3 R5      12V ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ K٢ 120Ω ‫א‬‫א‬ ‫א‬ ‫א‬، 5mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٣ ‫؟‬‫א‬‫א‬‫א‬ A + VS  R3 5 mA  A   − R1    A R2 - ٨٤ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    W‫א‬‫א‬‫א‬ R T ‫א‬‫א‬ K٤  1000 Ω ، 500 Ω EF  56 Ω ، 47 Ω EF  10 kΩ ، 2.2 kΩ ،1.5 kΩ EF  2.2 MΩ ،1 kΩ ، 470 kΩ ،1 MΩ EF ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٥ R 2 = 10 Ω R 3 = 12 Ω    R4 =1Ω  R 3 = 2.2 kΩ  ( b) (a )   R 2 = 10 Ω R1 = 4.7 Ω R 1 = 25.6 kΩ      R 1 = 1 MΩ R 5 = 10 M Ω  R1 = 1 MΩ    R 2 = 560 kΩ R 3 = 5.6 MΩ (c) - ٨٥ -      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬، 100 mA ‫א‬‫א‬‫א‬‫א‬‫א‬ K٦  ‫؟‬‫א‬‫א‬ R 1 = 45 Ω + VS R 2 = 15 Ω − A R 3 = 90 Ω ، 25V   R 2 ‫א‬، 25mA  R1 ‫א‬‫ א‬‫א‬‫א‬‫א‬ K٧  ‫؟‬ R 2  A + VS R1 R2 − V R3 ، R1 = 10Ω ‫א‬، VS = 48V ‫א‬‫א‬‫א‬ K٨ ‫؟‬‫א‬‫א‬‫א‬‫ ؛‬R 3 = R 4 = 47Ω ، R 2 = 96Ω ، VS = 24V ‫א‬ R 2 = 5.6 kΩ ، R 1 = 4.7 kΩ ‫א‬‫א‬ K٩ ‫؟‬‫א‬   - ٨٦ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١٠  W‫؟‬ VS R 4 = 220Ω , R 5 = 47Ω & V5 = 1.124V  R 1 = 100Ω , R 2 = 56Ω , R 3 = 330Ω , R1  R2   I VS  R3 R5    R4  V  ، V1 = 4.69 V   R1 ‫א‬‫א‬ VS = 15 V ‫א‬‫א‬‫א‬K١١  ‫؟‬ R 1 = 1.5 kΩ  R 2  R 1 = 1.5 kΩ, V1 = 4.69 V  V + R1  R2 VS = 15V    −   I = 1.43mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١٢ ، V2 = 2V3 ، V1 = 2V2 ‫א‬‫א‬ ، VS = 15V  ‫؟‬ R 3 ، R 2 ، R1  - ٨٧ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫؟‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٣ R 1 = 15KΩ , R 2 = 10KΩ , R 3 = 6.8KΩ , R 4 = 2.2KΩ R1 a  R2  VS1 = 24V  R3 VS2 = 12V  R4   VS1 ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K١٤   ‫א‬‫א‬  ‫؟‬‫א‬‫א‬،a  W 2.16V  R1 ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K١٥  WK،E R 3 ‫א‬‫א‬F V3 ‫א‬،E V1 = 2.16V F R 4 = 220KΩ & R 3 = 560Ω , R 2 = 1KΩ , R 1 = 390Ω  VS2 A  R 2 = 1 kΩ R 1 = 390 Ω   I R 3 = 560 Ω VS1 R 4 = 220 Ω       - ٨٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬ VS2 ، VS1 = 15V   ‫א‬E١٥F‫א‬‫א‬‫א‬K١٦  KE V1 = 3.77V FW 3.77V  R1 ‫א‬‫א‬ ‫א‬‫א‬ R1 ‫א‬‫א‬ VS2 ‫א‬ K١٧  ‫א‬‫א‬‫א‬ VS2 ‫א‬EE١٥F‫א‬‫א‬F R 2 ‫؟‬‫א‬‫א‬‫א‬ V4 ، V3 ، V2 ، V1 ‫א‬‫א‬،E١٦F  F  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٨ ‫؟‬ A, B, C, D ‫א‬‫א‬‫א‬‫א‬ ‫א‬E‫א‬  W R 1 = 12 kΩ, R 2 = 22 kΩ, R 3 = 47 kΩ & R 4 = 15 kΩ  d  c  R4  R3   b +  R2 VS = 48V − a R1  + V1 − ‫א‬‫א‬‫א‬ 560 Ω ‫א‬‫א‬‫א‬‫ א‬K١٩ ‫؟‬ R = 27 Ω ‫א‬‫א‬ - ٨٩ -       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    W‫א‬‫א‬‫א‬ A, B ‫א‬‫א‬ K٢٠  A  100 Ω +  56 Ω 12V   −   B  a  1kΩ A + 2.2kΩ 8V − 3.3kΩ B b - ٩٠ -  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ٦  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬     W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬ W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬   - ٩١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction ١J ٦ ،‫א‬‫א‬     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬KVoltage Drop‫א‬‫א‬  KVoltage Divider‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬ ،‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬،KCL  ‫א‬ Current Divider‫א‬  K‫א‬   Parallel Circuit‫א‬‫א‬‫א‬٢J ٦  Parallel Circuit‫א‬‫א‬‫א‬ ‫א‬ ‫א‬EF  ‫א‬‫א‬‫א‬ ‫א‬‫א‬E‫א‬F‫א‬‫א‬ ‫א‬‫א‬K  ‫א‬‫א‬E‫א‬F E١J ٦F‫א‬‫א‬‫א‬K‫א‬،‫א‬  K‫א‬‫א‬‫א‬  A I R1 I1 A I2 I R1 R2 B B ‫א‬‫א‬‫א‬EJ ١J ٦F - ٩٢ - I1 I2 R2       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    R1 A I I1 A  I I2 I1 R2 R1 I2  R2    B  B   I1 A R1 I A I I2 I1 R2 R1 R2 B B I2 R3 I2  K‫א‬‫א‬‫א‬E١J ٦F  Total Resistance (RT)‫א‬ ٢J ٢J ٥ ‫א‬،Parallel‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬ E١J ٦F 1 1 1 1 = + + ..... + R p R1 R2 RN  W‫א‬‫א‬‫א‬ E٢J ٦F     - ٩٣ -   RT = 1 1 1 1 + + .... R1 R2 RN  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W   ‫א‬‫א‬‫א‬  ‫א‬‫א‬ • K I T ‫א‬‫א‬‫א‬‫א‬ RT ‫א‬‫א‬  W‫א‬‫א‬‫א‬ RT ‫א‬‫• א‬   RT = R1 R2 R1 + R2 E ٣J ٦F  + VS −   R1  R2   K‫א‬‫א‬‫א‬EJ ١J ٦F ‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬ RT  ‫א‬‫א‬ •  W‫א‬‫א‬ RT = R N   R1 R2 R3     K‫א‬‫א‬‫א‬EJ ١J ٦F  ، R1 \ \ R2 W  ‫א‬‫א‬‫א‬ •  R1 \ \ R2 \ \..... \ \ R N W‫א‬‫א‬‫א‬،‫א‬‫א‬  - ٩٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Voltage Drop in Parallel Circuit‫א‬‫א‬‫א‬‫א‬‫א‬٣J ٦ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬   E١J ٦F  E٢J ٦F‫א‬‫א‬  VS =  25V R1 = R2 = 1.8kΩ 1kΩ F   R3 = R4 = 2.2kΩ 2.2kΩ R5 =  3.3kΩ    KE١J ٦F‫א‬‫א‬‫א‬E٢J ٦F  ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬  V1 = V2 = V3 = V4 = V5 = VS = 25V   Kirchhoff’s Current Law٤J ٦ W ‫א‬‫א‬ ‫א‬  ‫א‬‫א‬   K? ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬?  W‫א‬‫א‬    - ٩٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      EJ ٣J ٦F  ∑ I Entering = ∑ I Leaving  I (in ) + I in + I in3 + ..... + I inN 1 2  W‫א‬‫א‬ = I out 2 + I out 2 + .....I outN       EJ ٤J ٦F  EJ ٤J ٦F  W K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Node K‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬KE-F‫א‬‫א‬EHF‫א‬‫א‬‫א‬  EJ ٢J ٦F   W‫א‬‫א‬‫א‬‫א‬  R1  R2   R3  It     + Vs  KEJ ٢J ٦F‫א‬‫א‬‫א‬EJ ٣J ٦F - ٩٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬، I T ‫א‬‫א‬ Q ∑ I Entering = ∑I Leaving  ⇒ I t = I 1 + I 2 + .. I 3 + I N  EJ ٢J ٦F ،E٣J ٦F‫א‬‫א‬‫א‬ ‫א‬‫א‬  K A ‫א‬‫א‬‫א‬‫א‬‫א‬ A IT + VS −    I1 = 5mA I 2 = 12mA R1 R2   IT   B  KEJ ٢J ٦F‫א‬‫א‬‫א‬EJ ٣J ٦F  ‫א‬ ‫א‬ R1 ‫א‬‫א‬ 5mA ‫א‬‫א‬ A ‫א‬‫א‬‫א‬  W A ‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬12mA  I T = I1 + I 2  = 5mA + 12mA = 17mA  E٣J ٦F  KE٤J ٦F‫א‬ R 2 ‫א‬‫א‬‫א‬ IT = 100mA I1 = 30mA + VS − A R1   I2 R2  IT B   KE٣J ٦F‫א‬‫א‬‫א‬E٤J ٦F - ٩٧ - I 3 = 20mA R3    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  W‫א‬{ I T  A ‫א‬‫א‬‫א‬‫א‬‫א‬ I T = I1 + I 2 + I 3  ∴ 100mA = 30mA + I 2 + 20mA ⇒ I 2 = 100mA − 50mA = 50mA  E٤J ٦F ‫א‬ A1 , A 2 ‫א‬‫א‬‫א‬‫א‬  W‫א‬ x 5A + VS R1 − IT I3 A1  y    A2  R2 I1 = 1.5A R3 I 2 = 1A  KE٤J ٦F‫א‬‫א‬‫א‬E٥J ٦F  W 5A  x ‫א‬‫א‬‫א‬‫א‬‫א‬    ‫א‬ 5A = 1.5A + I A1  K A1 ‫א‬‫א‬‫א‬ I A1 W ∴ I A1 = 5 − 1.5 = 3.5A  K 3.5A ‫א‬‫א‬‫א‬ y ‫א‬‫א‬  ∴ 3 .5 A = 1 A + I A 2 ⇒ I A 2 = 3 .5 − 1 = 2 .5 A  W‫א‬‫א‬‫א‬∴  I A1 = 3.5A  I A 2 = 2.5A - ٩٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Total Parallel Resistors‫א‬‫א‬‫א‬‫א‬‫א‬٥J ٦ ‫א‬‫א‬‫א‬‫א‬١J ٥J ٦  ‫א‬‫א‬ R T ‫א‬‫א‬W  ‫א‬‫א‬‫א‬  ‫א‬‫א‬     K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I1 R1     I2 R2   IT  + VS − R1, R 2 ‫א‬‫א‬E٦J ٦F    ‫א‬F‫א‬‫א‬،‫א‬‫א‬ R1, R 2 ‫א‬‫א‬‫א‬‫א‬  W‫א‬ R T E‫א‬  W‫א‬،  I T = I1 + I 2 E٥J ٦F  W‫א‬‫א‬‫א‬‫א‬   VS VS VS E٦J ٦F = + R T R1 R 2  K VS ‫א‬‫א‬‫א‬   1 1 1 E٧J ٦F = + R T R1 R 2 - ٩٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬E٣J ٦F‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  W‫א‬   1 R + R2 E٨J ٦F = 1 R T R1 ∗ R 2  W   RT = R1 ∗ R 2 E٩J ٦F R1 + R 2  K‫א‬‫א‬‫א‬ R T    ‫א‬‫א‬ R T ‫א‬W I1 R1  I2 R2  I3 R3      IT   + VS −  R1, R 2 , R 3 ‫א‬‫א‬E٧J ٦F   W  IT = I1 + I2 + I3 E١٠J ٦F  W‫א‬   VS VS VS VS E١١J ٦F = + + R T R1 R 2 R 3  W‫א‬ VS  - ١٠٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     1 1 1 1 E١٢J ٦F = + + R T R1 R 2 R 3  W  RT = R1 ∗ R 2 ∗ R 3 E١٣J ٦F R1R 2 + R1R 3 + R 2 R 3   ‫א‬‫א‬‫א‬‫א‬ R T ‫א‬‫א‬  K ‫א‬‫א‬ R T ‫א‬‫א‬‫א‬  W‫א‬‫א‬  RT = 1 1 1 1 1 ( ) + ( ) + ( ) +K+ ( ) R1 R2 R3 Rn E١٤J ٦F - ١٠١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٥J ٦F  W‫א‬‫א‬ A, B ‫א‬ R T ‫א‬‫א‬  A R 1 = 100Ω B R 2 = 47Ω R 3 = 22Ω    KE٥J ٦F‫א‬‫א‬‫א‬E٨J ٦F  ‫א‬  WE١٣J ٦F‫א‬‫א‬‫א‬  RT = R1 ∗ R 2 ∗ R 3 R1R 2 + R1R 3 + R 2 R 3    RT = 100 ∗ 47 ∗ 22 = 13Ω 100 ∗ 47 + 100 ∗ 22 + 47 ∗ 22 ‫א‬‫א‬‫א‬‫א‬٢J ٥J ٦ ‫א‬‫א‬{ ‫א‬‫א‬‫א‬ ‫א‬‫א‬  W  Q R 1 = R 2 = R 3 = K = R n = R E١٥J ٦F 1 n  ∴ R T = R E١٦J ٦F  or R T = R E١٧J ٦F n  K‫א‬‫א‬‫א‬‫א‬‫א‬ R W ،‫א‬‫א‬ ‫א‬  K‫א‬‫א‬‫א‬ - ١٠٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٦J ٦F  K R T ‫א‬‫א‬‫א‬‫א‬ 8Ω   ‫א‬  W‫א‬‫א‬  RT = R 8 = = 2Ω n 4   Determining an unknown Parallel Resistor‫א‬‫א‬‫א‬٧J ٦ ،‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬‫א‬‫א‬ R T ‫א‬‫א‬‫א‬‫א‬  WEE٩J ٦FF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ RT = R1R 2 R1 + R 2 ‫א‬ R X ‫א‬ R A ‫א‬‫א‬  W‫א‬  RA   RX    RT  K‫א‬E٩J ٦F  ‫א‬ ‫א‬  R X ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W - ١٠٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    RT =  R AR X E١٨J ٦F RA + RX  R T (R A + R X ) = R A R X E١٩J ٦F  R T R A + R T R X = R A R X E٣٠J ٦F  R T R A = (R A − R T ) E٢١J ٦F  ∴R X = RTRA  E٢٢J ٦F RA − RT - ١٠٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٧J ٦F ‫א‬‫א‬‫א‬150Ω ‫א‬‫א‬  ‫؟‬‫א‬‫א‬‫א‬K 330Ω ‫א‬  R A = 330Ω    RX   KE٧J ٦F‫א‬‫א‬‫א‬E١٠J ٦F  ‫א‬ ‫א‬ 330Ω ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬ RT = RA RX 330 R X ⇒ 150 = RA + RX 330 + R X 150(330 + R X ) = 330 R X ⇒ 150 * 330 = 330 R X − 150 R X  ∴R X = 150 * 330 = 275Ω 180  E٨J ٦F  KE١١J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬ 10mA + VS   R 1 = 220Ω R 2 = 560Ω R 3 = 1kΩ −     KE٨J ٦F‫א‬‫א‬‫א‬E١١J ٦F - ١٠٥ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  R T ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  W RT = R1 ∗ R 2 ∗ R 3 R 1R 2 + R 1R 3 + R 2 R 3 RT = 220 ∗ 560 ∗ 1000 = 136Ω 220 ∗ 560 + 220 ∗ 1000 + 560 ∗ 1000  ∴ V = IT * R T = 10mA * 136Ω = 1.36V  E٩J ٦F   ‫א‬،1kΩ ‫א‬ R 3 = 680Ω ‫א‬‫א‬‫א‬  K IT = 10mA  ‫א‬  W R T ‫א‬‫א‬‫א‬‫א‬ RT = R1 ∗ R 2 ∗ R3 220 ∗ 560 ∗ 680 ⇒ RT = = 128Ω R1 R2 + R1 R3 + R 2 R3 220 ∗ 560 + 220 ∗ 680 + 560 ∗ 680  ∴ V = I T * R T = 10mA * 128Ω = 1.28V  Current Division in Parallel Circuits‫א‬‫א‬‫א‬‫א‬EF٦J ٦ {  ‫א‬‫א‬‫א‬‫א‬ R T ‫א‬‫א‬‫א‬‫א‬ ‫א‬KBranches‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬Current Divider Law‫א‬ ‫א‬ ، ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  W‫א‬،E١٢J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ١٠٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   I1 R1 I2 R2   I  + VS −  K‫א‬‫א‬‫א‬‫א‬E١٢J ٦F  W I ‫א‬ I1 , I 2 ‫א‬‫א‬‫א‬  V = I * R T E٢٣J ٦F  V = I1 * R 1 E٢٤J ٦F  V = I 2 * R 2 E٢٥J ٦F  W،‫א‬‫א‬،E٢٤J ٦F‫א‬E٢٣J ٦F‫א‬   I * R T = I1 * R 1 E٢٦J ٦F  I1 = I RT E٢٧J ٦F R1  W،‫א‬‫א‬،E٢٥J ٦FE٢٣J ٦F‫א‬  I2 = I RT E٢٨J ٦F R2 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬ Node ‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ - ١٠٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    IX = I  RT E٢٩J ٦F RX  K X = 1,2,3,K, n W  K‫א‬‫א‬‫א‬‫א‬‫א‬ W  K‫א‬‫א‬‫א‬‫א‬ W RT RX ‫א‬‫א‬‫א‬ X ‫א‬ X ‫א‬‫א‬ W IX  K‫א‬  EJ ١٠J ٦F  KE١٣J ٦F‫א‬Branch‫א‬ I1 R1 = 680Ω I2 R 2 = 330Ω I3 R 3 = 220Ω   10A   KE١٠J ٦F‫א‬‫א‬‫א‬E١٣J ٦F - ١٠٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ ‫א‬‫א‬‫א‬، 10A ‫א‬‫א‬‫א‬‫א‬ K‫א‬ R T ‫א‬‫א‬ RT = R1 ∗ R2 ∗ R3 R1 R2 + R1 R3 + R2 R3 RT = 680 ∗ 330 ∗ 220 = 111Ω 680 ∗ 330 + 680 ∗ 220 + 330 ∗ 220 I1 = I T RT 111 = 10 ∗ = 1.63A R1 680 I2 = IT RT 111 = 10 ∗ = 3.36A R2 330 I3 = IT RT 111 = 10 ∗ = 5.05A R3 220  W I 3 ‫א‬ I1 , I 2  I T = I1 + I 2 + I 3 10 = 1.63 + 3.36 + I 3 I 3 = 10 − (1.63 + 3.36) ∴ I 3 = 5.05A  ‫א‬‫א‬  ‫א‬‫א‬ K I1 = 1.63A  R1 = 680Ω ‫א‬‫א‬‫א‬K   ‫א‬K I3 = 5.05A  R 3 = 220Ω ‫א‬  K‫א‬  - ١٠٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬  W  IT I1 I2 R1 R2       K‫א‬‫א‬‫א‬‫א‬E١٤J ٦F  WE٩J ٦F‫א‬E٢٧J ٦F‫א‬‫א‬  I1 = I T RT R1    RT = R 1R 2 R1 + R 2  WE٢٧J ٦F‫א‬ R T   I1 = I T R1 E٣٠J ٦F R1 + R 2  W‫א‬‫א‬ I 2   I2 = IT R2 E٣١J ٦F R1 + R 2  I1 , I 2 ‫א‬‫א‬‫א‬‫א‬E٣١J ٦F،E٣٠J ٦F‫א‬‫א‬‫א‬ ‫א‬ I1 , I 2 , I 3 ‫א‬‫א‬،‫א‬‫א‬ R1, R 2 , R 3   W‫א‬‫א‬‫א‬ I1 R1 I2 R2 - ١١٠    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬               K‫א‬‫א‬‫א‬‫א‬EJ ١٥J ٦F  W‫א‬ R1 ‫א‬‫א‬ I1 ‫א‬  I1 = IT RT R1  ‫א‬‫א‬ R T ‫א‬‫א‬  RT = R1 ∗ R 2 ∗ R 3 E٣٢J ٦F R1R 2 + R1R 3 + R 2 R 3  W‫א‬‫א‬ R T   I1 = IT . R2 ∗ R3 E٣٣J ٦F R1R 2 + R1R 3 + R 2 R 3  W I 2 , I 3   I2 = IT . R1 ∗ R 3 E٣٤J ٦F R 1R 2 + R 1R 3 + R 2 R 3  I3 = IT . R1 ∗ R 2 E٣٥J ٦F R 1R 2 + R 1R 3 + R 2 R 3  EJ ١٠J ٦F  W‫א‬‫א‬‫א‬‫א‬‫א‬ R1=680Ω R2=330Ω - ١١١ R2=220Ω    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬          ‫א‬EJ ١٥J ٦F - ١١٢ -    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      RT =  ‫א‬ 1 = 111Ω ⎛ 1 1 1 ⎞ ⎜⎜ + ⎟⎟ + R R R 2 3 ⎠ ⎝ 1 RT I1 = I T = 1.63 A R1 R I 2 = T I T = 3.36 A  R2 R I 3 = T I T = 5.05 A R3  W،‫א‬‫א‬‫א‬E‫א‬F I T ‫א‬‫א‬  I1 + I 2 + I 3 = 10 A = I T  Power in Parallel Circuits‫א‬‫א‬‫א‬‫א‬٧J ٦  WE‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬ PT ‫א‬‫א‬‫א‬‫א‬‫א‬  PT = P1 + P2 + P3 + K + Pn E٣٦J ٦F   IT I2 I1 PT R1 P1 R2 P2 I3 R3 P3  K‫א‬‫א‬‫א‬‫א‬E١٦J ٦F  PT = V.I = I T2 .R T = In Rn Pn      V2  E٣٧J ٦F RT  W‫א‬  P1 = I12 .R 1 E٣٨J ٦F - ١١٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     P2 = I 22 .R 2 E٣٩J ٦F  P3 = I 32 .R 3 E٤٠J ٦F  PT = P1 + P2 + P3 E٤١J ٦F  KWatt‫א‬   E١١J ٦F  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   R 1 = 68 Ω R 2 = 33 Ω  R 3 = 22Ω     KE١١J ٦F‫א‬‫א‬‫א‬E١٧J ٦F  ‫א‬  ‫א‬‫א‬ RT = = R1 ∗ R 2 ∗ R 3 R 1R 2 + R 1R 3 + R 2 R 3 68 ∗ 33 ∗ 22 = 11.1Ω 68 * 33 + 68 * 22 + 33 * 22 Q PT = I T2 .R T = (2) 2 * 11.1 = 44.4W  ∴ PT = 44.4W - ١١٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬K ‫א‬‫א‬‫א‬  K‫א‬ VS = I.R T = 2 * 11.1 = 22.2V VS2 (22.2) 2 P1 = = = 7.25W .R 1 68 VS2 (22.2) 2 P2 = = = 14.9 W .R 2 33 VS2 (22.2) 2 P3 = = = 22.4 W .R 3 22 Q PT = P1 + P2 + P3 = 7.25 + 14.9 + 22.4  ∴ PT = 44.6W  KE‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  - ١١٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Summary‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬ ‫א‬‫א‬ I  R1 \ \ R2 \ \...... \ \ R N  R1 + R2 + .....RN  ‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬ RT =  ‫א‬‫א‬‫א‬ 1  W‫א‬‫א‬ 1 1 1 + + .... R1 R2 RN R .R RT = 1 2 R1 + R2  RT = R N   PT = P1 + P2 + P3 + .....PN  2 PT = Vs I T = I T RT = 2 V s RT RT = NR W‫א‬ PT = P1 + P2 + P3 + ...PN W‫א‬‫א‬ PT = VS I = I 2 , RT =   V 2S RT VS = V1 + V2 + ....V N Voltage Divider  Current Divider Ix = RT = R1 + R2    I T = I 1 + I 2 + ...... + I N   RT = R1 + R2 + ......R N       RT IT Rx  ‫א‬ I x VX = Rx V3 RT  ‫א‬ Vx  - ١١٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬    W‫א‬‫א‬‫א‬E١F  ‫א‬EF‫א‬EF  EF‫א‬EF  ‫א‬،‫א‬‫א‬ 100Ω ‫א‬1.2kΩ ‫א‬E٢F   R T ‫א‬  1.2kΩ 100Ω EF 1.2kΩ EF  90Ω EEF 90Ω 100Ω EF   ‫א‬‫א‬{‫א‬‫א‬ 68Ω ، 270Ω  330Ω E٣F  47Ω EF 668Ω EF  22Ω EF 68Ω EF  {،1kΩ ‫א‬‫א‬‫א‬‫א‬ E٤F  ‫א‬‫א‬  1kΩ EF 8kΩ EF   500Ω EF1kΩ EF   ‫א‬‫א‬‫א‬‫א‬E٥F  EFEF  ‫א‬‫א‬EFEF    ‫א‬‫א‬‫א‬‫א‬‫א‬E٦F  EF‫א‬‫א‬EF  EFEF - ١١٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    K 3A ‫א‬، 5A ‫א‬‫א‬‫א‬E٧F  ‫א‬‫א‬‫א‬  EF 2A EF  K‫א‬EF 8A EF   ‫א‬ ‫א‬،‫א‬‫א‬ 390 Ω, 560 Ω, 820 Ω ‫א‬‫א‬E٨F    560Ω EF 390Ω EF  K‫א‬EF 820Ω EF   ‫א‬‫א‬‫א‬‫א‬‫א‬E٩F  ‫א‬EF EF  EFEF‫א‬EF ‫א‬‫א‬EF   W‫א‬‫א‬‫א‬‫א‬‫א‬E١٠F  ‫א‬‫א‬‫א‬‫א‬‫א‬EF  ‫א‬‫א‬‫א‬‫א‬EF  E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬EF  K‫א‬EF   ‫א‬‫א‬‫א‬،1W ‫א‬‫א‬‫א‬‫א‬E١١F  4W EF1W EF  16W EF 0.25W EF  - ١١٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬ R3 ‫א‬E١٢F R1  R2 I VS 680Ω I 1kΩ R3=? R4 I =10mA 320Ω R5    1.5kΩ   ‫א‬‫א‬‫א‬‫א‬‫א‬E١٣F  5.6KΩ  5.6KΩ Vs  5.6 K Ω   B,A ‫א‬ 10V  R1 ‫א‬‫א‬‫א‬E١٤F  A 10V Vs R1 R2 B 100Ω C - ١١٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬E١٥F  K‫א‬‫א‬ V1 ?  V2 ? V3 ? R V4 ? 100V  V1 V4 V2  V3   4R 7.5mA  1mA 2mA + R1 50Ω   W‫א‬‫א‬‫א‬E١٦F   0.5mA R2 ٣R  R4      R2 , R3 , R4 ‫א‬  10mA  W‫א‬‫א‬‫א‬ RT ‫א‬‫א‬‫א‬E١٧F R3 3.3kΩ R1 1kΩ R2 2.2kΩ - ١٢٠ - R4 5.6kΩ  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٨F   10mA  R3 3.3kΩ R1 1kΩ R2 2.2kΩ  R4 5.6kΩ     -   + W‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬E١٩F  10V - - ١٢١ - R1 R2 33Ω Ω33  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  E‫א‬J ‫א‬F‫א‬ E‫א‬-‫א‬F ‫א‬ ٧  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     E‫א‬-‫א‬F‫א‬W‫א‬‫א‬  KE‫א‬-‫א‬F‫א‬‫א‬W‫א‬‫א‬   K‫א‬J ‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬     W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬ W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬             - ١١٦ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬      Introduction ١J ٧ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    ‫א‬‫א‬–‫א‬‫א‬‫א‬٢J ٧ ‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬‫א‬–‫א‬‫א‬‫א‬ K‫א‬‫א‬–‫א‬‫א‬‫א‬EJ ١J ٧F‫א‬‫א‬ ‫א‬‫א‬E‫א‬–‫א‬F‫א‬‫א‬‫א‬  W‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W  K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬W  K RT ‫א‬‫א‬‫א‬‫א‬‫א‬   EJ ١J ٧F  KEJ ١J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬        - ١١٧ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬      R2  R1  R3 R6 R8 R5  R4   R7 R9    KEJ ١J ٧F‫א‬‫א‬‫א‬EJ ١J ٧F  ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ R 1 , R 7 ‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬K‫א‬  W‫א‬‫א‬‫א‬‫א‬ ( R8 // R9 ), ( R4 // R5 // R6 ), ( R2 // R3 )  R T = R1 + R 2 // R 3 + R 4 // R 5 // R 6 + R 7 + R 8 // R 9   W R T = R1 + R 2R 3 R 4R 5R 6 R 8R 9 + + R7 + R 2 + R 3 R 4R 5 + R 4R 6 + R 5R 6 R8 + R9  - ١١٨ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     EJ ١J ٧F  W‫א‬‫א‬‫א‬‫א‬‫א‬   R1 A   - R2 Vs  R3 +   D  EJ ١J ٧F‫א‬‫א‬‫א‬EJ ١J ٧F  ‫א‬ A , D‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  W،‫א‬‫א‬‫א‬  A → D ⇒  RT = R1 + (R2 \ \ R3 ) = R1 + ( R 2 R3 R 2 + R3   R1 ‫א‬‫א‬‫א‬،‫א‬ R3 , R2   EJ ١J ٧F  W‫א‬‫א‬A,B‫א‬، RT ‫א‬‫א‬   R1 R2 C D  R4  R3 E    B  EJ ١J ٧F‫א‬‫א‬‫א‬EJ ١J ٧F - ١١٩ -   ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     ‫א‬  RT = (R1 // R2 ) + (R3 // R4 )   E٢J ٧F  K‫א‬‫א‬‫א‬‫א‬،E٢J ٧F‫א‬‫א‬‫א‬    R1 IT + VS − I3 A R3 R4 IT  I2 R2 B  KE٢J ٧F‫א‬‫א‬‫א‬E٢J ٧F      ‫א‬    R1 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K R 3 ‫א‬‫א‬، R 2 ، A ‫א‬  R1, R 4 ‫א‬‫א‬K R 4 ‫א‬‫א‬ B ‫א‬  ‫א‬، R 2 // R 3 ، ‫א‬‫א‬ R 2 , R 3 ‫א‬K‫א‬‫א‬  W R T ‫א‬ R T = R1 + R 2 // R 3 + R 4  - ١٢٠ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     E٣J ٧F    KE٣J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  R1  + VS R2 − R4 R3    R5     KE٣J ٧F‫א‬‫א‬‫א‬E٣J ٧F  ‫א‬  KE٤J ٧F‫א‬‫א‬‫א‬‫א‬  R1  + VS R2 R3    − R4 R5      KE٤J ٧F‫א‬‫א‬‫א‬E٣J ٧F  ‫א‬،‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬ R T ‫א‬ RT = R1 + ( R2 // R3 ) + ( R4 // R5 ) - ١٢١ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     E٤J ٧F  KE٥J ٧F‫א‬ A, D ‫א‬‫א‬‫א‬‫א‬‫א‬ R2 R1   R3  A  R4 R6   D R5  KE٤J ٧F‫א‬‫א‬‫א‬E٥J ٧F   ‫א‬ ‫א‬ R 2 , R 3 ‫א‬‫א‬‫א‬‫א‬ R T1 ‫א‬‫א‬  W R 4 ‫א‬‫א‬‫א‬ R T1 = (R 2 + R 3 ) ⋅ R 4 (R 2 + R 3 ) + R 4   KE٦J ٧F R 5 ‫א‬‫א‬ R T1 ‫א‬‫א‬  A R T1 R1 R6 R5 D  KE٤J ٧F‫א‬‫א‬‫א‬E٦J ٧F       W‫א‬‫א‬ D, A ‫א‬‫א‬‫א‬‫א‬ R T = R1 + R 6 //( R T1 + R 5 )  - ١٢٢ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     E٥J ٧F  K A, B, C ‫א‬‫א‬‫א‬‫א‬،E٧J ٧F‫א‬‫א‬‫א‬  B   R1 R2   A  R3  C  KE٥J ٧F‫א‬‫א‬‫א‬E٧J ٧F  ‫א‬ ‫א‬‫א‬ R 2 , R 3  A, B ‫א‬‫א‬‫א‬  W R T ‫א‬‫א‬ R1 ‫א‬‫א‬  fromA → B : R1 \ \ (R2 + R3 ) R TAB = R 1 * (R 2 + R 3 ) R 1 + (R 2 + R 3 )  W B, C  A, C ‫א‬‫א‬  fromA → C : (R1 + R2 ) \ \ R3  R TAC = (R 1 + R 2 ) * R 3 (R 1 + R 2 ) + R 3 fromB → C : (R1 + R3 ) \ \ R2 R TBC = (R 1 + R 3 ) * R 2 (R 1 + R 3 ) + R 2     - ١٢٣ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     Analysis of Series-Parallel Circuits‫א‬‫א‬–‫א‬‫א‬‫א‬ ٣J ٧ Total Resistance ‫א‬‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬، ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦    EJ ٦J ٧F  W‫א‬‫א‬ RT ‫א‬‫א‬ R1 A   10Ω - R2 Vs 100Ω +  B  W‫א‬  R3 100 Ω    ‫א‬ RT ‫א‬‫א‬ R1 + (R2 \ \ R3 )   R2−3 = R = 50Ω ⇐ ‫א‬‫א‬ R3 , R2 W‫א‬ 2  ∴ RT = R1 + R2 −3 = 60Ω W R2−3 ‫א‬ R1  - ١٢٤ -   ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     EJ ٦J ٧F  W‫א‬‫א‬‫א‬ RT ‫א‬‫א‬   R3 R1  30Ω 10Ω A   C R2  20Ω  (1) fromAtoB  (3) fromBtoC  (2) fromAtoC   ‫א‬ WBA‫א‬‫א‬‫א‬‫א‬ K١ R1 A B    R2 R1 \ \ (R2 + R3 ) ⇒ R AB = C  R3 R1 .(R2 + R3 ) = 8.33Ω R + R + R2 WCA‫א‬‫א‬‫א‬‫א‬ K٢ R2 A C    R1 R 2 \ \ (R1 + R3 ) ⇒ R AC = R2 * (R1 + R3 ) = 13.33Ω R2 + R1 + R3 B - ١٢٥ - R3   ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬    WCB‫א‬‫א‬‫א‬‫א‬ K٣ R3 B  C   R1 R3 \ \ (R1 + R2 ) ⇒ R BC = A  R2  R3 (R1 + R 2 ) = 15Ω R3 + R1 + R2  ‫א‬‫א‬ (R AB ) B,A‫א‬‫א‬‫א‬‫א‬   K (RCB ) C,B (R AC ) C,A   EJ ٦J ٧F  KE٨J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 = 47Ω R 3 = 47Ω A + VS − R 1 = 100Ω R 4 = 68Ω B R 6 = 75Ω  R 5 = 39Ω  KEJ ٦J ٧F‫א‬‫א‬‫א‬E٨J ٧F  ‫א‬  ‫א‬‫א‬ R 2 , R 3 ‫א‬ R T2,3 = 47 + 47 = 94Ω  - ١٢٦ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     R 6 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R 4 , R 5 ‫א‬‫א‬ R T4,5, 6 = 68 * 39 + 75 = 99.8Ω 68 + 39  W  ‫א‬‫א‬‫א‬‫א‬ 99.8Ω , 94Ω ‫א‬  99.8 * 94 = 48.41Ω 99.8 + 94 R TA , B =  94Ω 100Ω + VS  B A  99.8Ω   −  EJ ٦J ٧F‫א‬‫א‬‫א‬E٩J ٧F ∴ R AB = 48.41Ω  ∴ R T = 100Ω + 48.41Ω = 148.41Ω  EJ ٦J ٧F  KE٢٠J ٧F‫א‬‫א‬‫א‬‫א‬ R 5 = 50Ω R 3 = 50Ω R 2 = 100Ω R 4 = 100Ω R 6 = 100Ω R1 = 50Ω  KEJ ٦J ٧F‫א‬‫א‬‫א‬E١٠J ٧F - ١٢٧ -  R 7 = 100Ω   ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     ‫א‬  Q R 6 // R 7 ∴ R 6, 7 = 100 * 100 = 50Ω 100 + 100  W‫א‬ R 6,7 ‫א‬‫א‬ R 5 R 5 + R 6,7 = 50 + 50 = 100Ω  R 4 //(R 5 + R 6 // R 7 ) = 100 // 100 = 50Ω  K‫א‬‫א‬ R 3 ‫א‬‫א‬‫א‬‫א‬ R 3 + R 4 //( R 5 + R 6 // R 7 ) = 50 + 50 = 100Ω  W، R 2 ‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 //[R 3 + R 4 //(R 5 + R 6 // R 7 )] = 100 * 100 = 50Ω 100 + 100   R T ‫א‬ R1 ‫א‬‫א‬‫א‬‫א‬‫א‬ R T = 50 + 50 = 100Ω  Current‫א‬W Total Current‫א‬‫ א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W، I T ‫א‬‫א‬ RT ‫א‬‫א‬‫א‬  IT = - ١٢٨ - Vs RT   ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     E٧J ٧F  KE١١J ٧F‫א‬‫א‬‫א‬‫א‬ IT Rc A Ra  B  VS R b  C RL Rd  D  KE٧J ٧F‫א‬‫א‬‫א‬E١١J ٧F ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬  W  K R d // R L ‫א‬‫א‬ R d , R L    R C + R d // R L  R C ‫א‬‫א‬‫א‬ ‫א‬ R b ‫א‬‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬ R b //[R C + (R d // R L )]  W‫א‬ ‫א‬، R a ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  R T = R a + R b //[R C + (R d // R L )] - ١٢٩ -  W‫א‬‫א‬‫א‬  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     W ‫א‬‫א‬‫א‬ R T ‫א‬‫א‬  IT  A Ib Ra Ic Rc   B + VS Rb −   Rd Id C RL IL    D  KE٧J ٧F‫א‬‫א‬‫א‬E١٢J ٧F  W‫א‬‫א‬‫א‬‫א‬ Ia = IT IT = Ib + IC IC = Id + IL ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬D‫א‬  W I T ‫א‬ IT = I b + Id + I L   Branch Current‫א‬‫א‬‫א‬‫ א‬K E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K ‫א‬  K‫א‬‫א‬ - ١٣٠ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     EJ ٨J ٧F  KEJ ١٣J ٧F I1 , I 2 , I 3 .I 4 ‫א‬‫א‬ IT  I2 A  R2=330 Ω I1 Vs 560 + R3 I3 Ω 50V  B R1 -  R4= 560 Ω  330 I4  C   EJ ٨J ٧F‫א‬‫א‬‫א‬EJ ١٣J ٧F  ‫א‬  W‫א‬‫א‬‫א‬‫א‬  R1 \ \[R2 + (R3 \ \ R4 )]  W R1 ‫א‬‫א‬   I1 = : .V1 = VS  ‫א‬‫א‬ VS 50V = = 89mA R1 560Ω W I 2 E٢F  W‫א‬‫א‬‫א‬K  W{ R2−3− 4 ‫א‬  R 2 + ( R3 \ \ R 4 ) ⇒ R 2 − 3 − 4 = R 2 + R 3 .R 4 = (330Ω ) + (207.6Ω ) = 538Ω R3 + R 4  W،    ⇒ I2 = V2 50V = = 93mA R2−3− 4 538Ω  W RT ‫ ﺣﺴﺎب ﻗﻴﻤﺔ اﻟﻤﻘﺎوﻣﺔ اﻟﻜﻠﻴﺔ‬.‫ب‬ - ١٣١ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬    R1 \ \ R 2 −3− 4 ⇒ RT =  R1 .R 2 −3− 4 560 * 538 = = 274.4Ω R1 + R2 −3− 4 560 + 538  W I T ، RT   W I T ‫א‬‫א‬  IT = VS 50 = = 182mA RT 274.4  W I 2   ∑ I Entering = ∑ I Leaving ∴ I T = I 1 + I 2 ⇒ I 2 = I T − I 1 = (182 − 89)mA = 93mA  W I 3 , I 4 E٣F  E‫א‬‫א‬F‫א‬‫א‬K I3 = R3− 4 R I 2  and I 4 = 3− 4 I 2 R3 R4 R3− 4 = ⎧ I 3 = 58.5mA.⎫ R3 R4 = 207.6Ω ⇒ ⎨ ⎬ R3 + R 4 ⎩ I 4 = 34.5mA ⎭  W I 4 = I 2 − I 3 ‫א‬ I 4    I 3   Voltage divider‫א‬ R4 , R3  VCB ‫א‬K  ⇒ V BC =  R3− 4 207.6Ω * VS = * 50 = 19.3V (330 + 207.6Ω ) R 2 + R3 − 4   I 3 , I 4     V BC == 58.5mA R3 V I 4 = BC = 34.5mA R1 I3 =  W،‫א‬ V AC K ( ) V 2 = V AB = I 2 * R 2 = 93 * 10 −3 * 330 = 30.7V W R2  V AB   V BC = V S − V AB = 50 − 30.7 = 19.3V W - ١٣٢ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     W، I 4 , I 3 ‫א‬ VCB V CB = 34.5mA = 58 .5 mA  and I 4 = R4 R3 I3 =   EJ ٨J ٧F  KE١٠J ٧F R 3 ‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬ IT  R1 = 1kΩ + VS = 22V  R 2 = 2.2kΩ I2 I3  R 3 = 3.3kΩ −  KEJ ٨J ٧F‫א‬‫א‬‫א‬EJ ١٣J ٧F  ‫א‬ ‫א‬‫א‬‫א‬‫א‬{ R 3  R 2 ‫א‬‫א‬  K A ‫א‬‫א‬  K R T ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R T = R1 + R 2R 3 R2 + R3 R T = 1kΩ + (2.2kΩ)(3.3kΩ) 2.2kΩ + 3.3kΩ ∴ R T = 1kΩ + 1.32kΩ = 2.32kΩ ∴ R T = 2.32kΩ IT = VS 22V = = 9.48mA R T 2.32kΩ - ١٣٣ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬ I 2 = 9.48mA * 3.3kΩ = 5.69mA 5.5kΩ W I 3 = 9.48mA * 2.2kΩ = 3.79mA 5.5kΩ  EJ ٨J ٧F   VS = 50V ‫א‬‫א‬‫א‬‫א‬ R 4 ‫א‬‫א‬‫א‬ I2 I1 + VS = 50V    R2 R1 330Ω A 560Ω I3 − R3 330Ω  KEJ ٨J ٧F‫א‬‫א‬‫א‬EJ ١٣J ٧F  I4  R4 560Ω  ‫א‬ ‫א‬‫א‬، 50V ‫א‬‫א‬‫א‬‫א‬  K R 3 , R 4 ‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬ R1 ‫א‬  W‫א‬‫א‬‫א‬ R 4 ‫א‬‫א‬ I 4 ‫א‬  K R 2 , R 3 , R 4 ‫א‬‫א‬‫א‬W  K R 2 , R 3 , R 4 ‫א‬‫א‬‫א‬ I 2 W  K‫א‬ I 4 ‫א‬ A ‫א‬ I 2 W R T2,3, 4 = R 2 + R 3 // R 4 - ١٣٤ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬ = R2 + R 3R 4 R3 + R4 = 330 + 330 * 560 = 538Ω 330 + 560    ∴ R T2,3, 4 = 538Ω  W I2 = 50 = 93mA 538  W‫א‬‫א‬ ⎛ R3 I 4 = I 2 ⎜⎜ ⎝ R3 + R4 ⎞ ⎟⎟ = 34.5mA ⎠ ∴ I 4 = 34.5mA Voltage Drops‫א‬‫א‬W     ‫א‬،‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  E٩J ٧F ‫א‬،EJ ١٤J ٧F‫א‬‫א‬‫א‬ A ‫א‬‫א‬‫א‬‫א‬  K R1 ‫א‬‫א‬ - ١٣٥ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬      R1 = 150Ω  A + VS = 80V R 2 = 560 Ω − R 3 = 560 Ω    B  KE٩J ٧F‫א‬‫א‬‫א‬EJ ١٤J ٧F    ‫א‬ ‫א‬،‫א‬‫א‬ R 2 , R 3 ‫א‬‫א‬  WK‫א‬‫א‬ R T2,3 = 560 * 560 = 280Ω 560 + 560  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ RTAB = 1 (560) = 280Ω 2  W‫א‬‫א‬‫א‬‫א‬، R1 ‫א‬‫א‬‫א‬ 280Ω ‫א‬  R1 = 150Ω A   + VS = 80V  280Ω  − B  KE٩J ٧F‫א‬‫א‬‫א‬EJ ١٤J ٧F - ١٣٦ -    ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     W R T ‫א‬‫א‬‫א‬ R T = 150 + 280 = 430Ω   V AB ‫א‬‫א‬ ⎛R ⎞ V AB = ⎜⎜ AB ⎟⎟V S ⎝ RT ⎠  K‫א‬‫א‬ R AG  ⎛ 280 ⎞ V AB = ⎜ ⎟ * 80 = 52.1V ⎝ 430 ⎠   R1 ‫א‬‫א‬  V S = V1 + V AB  V1 = V S − V AB = 80 - 52.1 = 27.9V ∴ V1 = 27.9V  E١٠J ٧F  EJ ١٤J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬   R1 = 1kΩ IT = 1mA + VS −  I1 I2   R 2 = 2.2kΩ I3 R 3 = 3.9kΩ R 4 = 1.5kΩ I4 R 5 = 560Ω  KE١٠J ٧F‫א‬‫א‬‫א‬EJ ١٤J ٧F - ١٣٧ -       ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     ‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   R1 ‫א‬‫א‬K  ‫א‬‫א‬ R1, R 2 ‫א‬‫א‬‫א‬  W‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬ ⎛ R2 I1 = I T ⎜⎜ ⎝ R1 + R 2 ⎞ ⎟⎟ ⎠ ⎛ 2.2kΩ ⎞ = 1mA⎜ ⎟ = 688µA ⎝ 1kΩ + 2.2kΩ ⎠ ∴ I1 = 688µA   R1 ‫א‬‫א‬‫א‬ V1 = I1 .R 1 = 688µA * 1kΩ V1 = 688mV  W‫א‬ R 3 ‫א‬ I 3 ‫א‬ ⎛ ⎞ R 4 + R5 ⎟⎟ I3 = IT ⎜⎜ R + ( R + R ) 4 5 ⎠ ⎝ 3  W‫א‬ I T  I3 = 346µA  W R 3 , R 4 , R 5 ‫א‬‫א‬‫א‬ V3 = I 3 .R 3 = (346µA)(3.9kΩ) ∴ V3 = 1.35V  W، R 4 ‫א‬‫א‬ V4  I 4 = I5 = IT − I3 = 1mA - 346µA - ١٣٨ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     = 1mA - 0.346mA  ∴ I 4 = 0.654mA  V4 = (0.654mA)(1.5kΩ) = 0.981V ∴ V4 = 981mV  V5 = I 5 * R 5 = 366mV  E١١J ٧F  KE١٥J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   R 1 = 3.3kΩ  B A   R 3 = 1kΩ + VS = 8V −  C R 2 = 6.2kΩ R 4 = 1kΩ D  KE١١J ٧F‫א‬‫א‬‫א‬E١٥J ٧F R 5 = 680Ω  R 6 = 390Ω      ‫א‬   ، ‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬  ،‫א‬‫א‬‫א‬E١٥J ٧F‫א‬  W A, B ‫א‬‫א‬RAB‫א‬‫א‬‫א‬ R AB = R1R 2 = 2.15kΩ R1 + R 2  W C, D ‫א‬‫א‬RCD‫א‬‫א‬‫א‬‫א‬ - ١٣٩ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬ R CD =   R 4 (R 5 + R 6 ) = 517Ω R4 + R5 + R6    ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  KE١٦J ٧F R AB = 2.15kΩ + VS = 8V R 3 = 1kΩ − R CD = 517Ω       KE١١J ٧F‫א‬‫א‬‫א‬E١٦J ٧F W‫א‬‫א‬‫א‬‫א‬ ⎛R ⎞ VAB = ⎜⎜ AB ⎟⎟VS = 4.69V ⎝ RT ⎠ ⎛R VCD = ⎜⎜ CD ⎝ RT ⎞ ⎟⎟VS = 1.13V ⎠ ⎛R ⎞ V3 = ⎜⎜ 3 ⎟⎟VS = 2.18V ⎝ RT ⎠  W‫א‬‫א‬ ⎛R ⎞ VAB = V1 = V2 = 4.69V⎜⎜ AB ⎟⎟VS = 4.69V ⎝ RT ⎠  K (R 5 + R 6 ) ‫א‬‫א‬ R 4 ‫א‬ VCD ‫א‬ ⎛ R5 V5 = ⎜⎜ ⎝ R5 + R6 ⎞ ⎟⎟VCD = 718mV ⎠ - ١٤٠ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬   ⎛ R6 V6 = ⎜⎜ ⎝ R5 + R6  ⎞ ⎟⎟VCD = 412mV ⎠  ‫א‬‫א‬‫א‬‫א‬‫ א‬٤J ٧ K ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬ ‫א‬K  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬E١٢J ٧F   E١٢J ٧F  W‫؟‬‫א‬،E١٧J ٧F‫א‬‫א‬‫א‬ V1 = 12V, V2 = 8V, V3 = 8V, V4 = 5V  R1   + VS − R2 R3 R4     KE١٢J ٧F‫א‬‫א‬‫א‬E١٧J ٧F   ‫א‬  ‫א‬  VS ‫א‬، ‫א‬  W‫א‬‫א‬ VS = V1 + V2 + V4 = 12 + 8 + 5 = 25V  - ١٤١ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     E١٣J ٧F  W، VS  V4 = 28.2V ‫א‬W‫א‬‫א‬‫א‬ R1 = 2.7kΩ, R2 = 2.2kΩ, R3 = 5.6kΩ, R4 = 10kΩ, R5 = 15kΩ, R6 = 820Ω  R1 IT I1 + VS IT I2 R2 I3 − R3 R6 IT  I5 I4 R4 R5    KE١٣J ٧F‫א‬‫א‬‫א‬E١٨J ٧F  ‫א‬  W،‫א‬ I T = I3 + I 4 + I5 ، R 3 , R 4 , R 5 ‫א‬ ‫א‬ V4 = 28.2V  W I 3 , I 4 , I 5 ‫א‬‫א‬ I4 = 28.2 = 2.82mA 10k I5 = 28.2 = 1.88mA 15k I3 = 28.2 = 5.04mA 5.6k ∴ I T = 5.04mA + 1.88mA + 2.82mA = 9.74mA - ١٤٢ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     R eq ‫א‬‫א‬ I T   W I T  R 3 , R 4 , R 5  IT = V4 R eq  W R eq = ∴IT = R 3R 4 R 5 = 2.896kΩ R 3 R 4 ,+ R 3 R 5 + R 4 R 5 28.2 2.896 * 10 3 = 9.74mA  K‫א‬‫א‬   R1 // R 2 ‫א‬‫א‬‫א‬‫א‬ V1 = V2 = I T (R 1 // R 2 )  = IT ( R 1R 2 ) R1 + R 2  W‫א‬‫א‬ V1 = V2 = 11.8V   R 6 ‫א‬‫א‬ V6 = I T .R 6 = 9.74 * 10 −3 * 0.82 * 10 3  ∴ V6 = 7.99V   VS ‫א‬ VS = V1 + V4 + V6  = 11.8 + 28.2 + 7.99 = 48V  ∴ VS = 48V - ١٤٣ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     W   ‫א‬‫א‬ VS E١F  K‫א‬‫א‬ ‫א‬   VS ‫א‬‫א‬‫א‬ VS E٢F  W VS = IT * R T                  - ١٤٤ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     Summary‫א‬ ‫א‬‫א‬‫א‬E‫א‬–‫א‬F‫א‬‫א‬‫א‬E١F  K‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬E٢F  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣F  E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤F ⎛R ⎞ VX = VS ⎜⎜ X ⎟⎟ ⎝ RT ⎠   W  ‫א‬‫א‬‫א‬W R X   ‫א‬‫א‬‫א‬W VX   ‫א‬W VS   K‫א‬‫א‬‫א‬W R T   ‫א‬E ‫א‬‫א‬F‫א‬E٥F  K‫א‬Common Reference Point - ١٤٥ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١ R1 = 56Ω    + VS = 1.5V R 3 = 100Ω R 2 = 100Ω −   R 4 = 27Ω    (a)   R1 + VS = 3V  680Ω − R2 R3 680Ω 330Ω R 3 = 3.3kΩ R 4 = 10kΩ R 5 = 5.6kΩ   - ١٤٦ - (c )    R 2 = 6.2kΩ R 1 = 1kΩ 180Ω   (b) + 5V − R4          ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     K‫א‬‫א‬‫א‬١‫א‬‫א‬‫א‬‫א‬K٢  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬K٣  ‫א‬‫א‬‫א‬‫א‬‫א‬  R 2 = 1kΩ  − R 1 = 1kΩ 1V  R 4 = 3.3kΩ R 3 = 2.2kΩ +  W‫א‬‫א‬ (A, B) ‫א‬‫א‬J ٤ R1 = 1kΩ  R 2 = 330Ω  R 5 = 1kΩ R 3 = 470Ω + 100V − R 6 = 1.5kΩ B A R 4 = 560Ω R 7 = 680Ω R 8 = 100Ω  W‫א‬‫א‬J ٥ R2 P = 20 W + 4A 20V 40V − R5 1A R7 5V R6 1V R8 1A - ١٤٧ -  P = 2W R1 R4 R3    ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J ٦ ‫א‬، R L = 10kΩ ‫א‬KE (A, B) ‫א‬FNo Load‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬   R 1 = 10kΩ + 22V  A −  R 2 = 5.6kΩ RL R 3 = 2.7 kΩ B   W‫א‬‫א‬J ٧   R T ‫א‬‫א‬‫א‬EF  I T ‫א‬‫א‬‫א‬‫א‬EF   910Ω ‫א‬‫א‬EF  K VA , VB  A, B ‫א‬EF + 56Ω  56Ω  60V  910Ω − 1kΩ A 1kΩ 560kΩ 1kΩ - ١٤٨ -  B 1kΩ 560kΩ   ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬     WLadder Network‫א‬‫א‬‫א‬J ٨  R T ‫א‬‫א‬EF  VA ،A‫א‬‫א‬EF  VB ،B‫א‬‫א‬ R1 = 5.6kΩ A R 3 = 1kΩ B R 2 = 2.2kΩ 18V  R 5 = 1kΩ R 4 = 2.2kΩ  R 6 = 1kΩ    ‫א‬‫א‬‫א‬‫א‬  A, B ‫א‬‫א‬‫א‬‫א‬J ٩  W‫א‬ R 3 = 220Ω R1 = 100Ω A + − B I2 IT R 2 = 820Ω I3 I5 I4  R 4 = 820Ω R 6 = 680Ω  R 9 = 100Ω IT  R 5 = 100Ω  R 8 = 220Ω R 7 = 100Ω  ‫א‬١٠‫א‬‫א‬‫א‬‫א‬‫א‬J ١٠  ‫؟‬ VS = 10V ،10V A, B ‫א‬‫א‬    - ١٤٩ -  ‫א‬‫א‬  ١١١  ‫א‬  E‫א‬-‫א‬F‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬J ١١  W‫א‬‫א‬‫א‬ R 1 = 10kΩ, R 2 = 20kΩ, R 3 = 60kΩ, R 4 = 15kΩ, R 5 = 5kΩ   R3 + VC R4 B R1 R5 A R2 VA  VB 100V −  C - ١٥٠ -   ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ٨  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٣ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬ W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   - ١٥٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction  ١J ٨ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬K  ‫א‬  K‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬ KEAlternating Current‫א‬‫א‬‫א‬F‫א‬،‫א‬‫א‬‫א‬ ‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬‫א‬‫א‬‫א‬ ٢J ٨ Voltage Source‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،Current Source  K‫א‬ Constant Voltage Source ‫א‬‫א‬ ١J ٢J ٨ ‫א‬‫א‬    ‫א‬‫א‬‫א‬ J ٨F‫א‬‫א‬‫א‬‫א‬ RS ‫א‬‫א‬  KE١ +  RS VS RL −      E١J ٨F - ١٥١ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     R S ،Ideal Voltage Source ‫א‬‫א‬  W‫א‬‫א‬   R L >> R S E١J ٨F  Constant Current Source  ٢J ٢J ٨ ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬‫א‬ R S  KE٢J ٨F،  A iS   RS A   B  EJ ٢J ٨F  iS A A   RL RS   B  EJ ٢J ٨F  R S ،Ideal Current Source ‫א‬‫א‬  W‫א‬‫א‬  E٢J ٨F   R S >> R L ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬  - ١٥٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Source Conversions ‫א‬ ٣J ٢J ٨ ‫א‬،‫א‬‫א‬‫א‬  K‫א‬E٣J ٨F‫א‬ A A + iL RS VS RL − ≡  i L iS  RS I RL   B B  KE٣J ٨F   W IL ‫א‬‫א‬‫א‬  E٣J ٨F   IL = VS RS + R L  W IL ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  E٤J ٨F  ⎛ RS ⎞ ⎟⎟iS I L = ⎜⎜ + R R L⎠ ⎝ S   WE٤J ٨FE٣J ٨F‫א‬‫א‬  E٥J ٨F  - ١٥٣ -  VS = R S ⋅ i S  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١J ٨F  W‫א‬‫א‬‫א‬‫א‬ (a )R L = 100Ω  (b)R L = 560Ω  (c)R L = 1KΩ A iL iS 1A I RL RS 10kΩ     B  KE١J ٨F‫א‬‫א‬‫א‬E٤J ٨F   ‫א‬  R L = 100Ω   IL ،E٣J ٨F ⎛ R ⎞ S ⎟⎟iS  I L = ⎜⎜ + R R L⎠ ⎝ S 10kΩ ⎞  I L = ⎛⎜ ⎟ * 1 = 990mA = 0.99A ⎝ 10.1kΩ ⎠  W، R L = 560Ω  10kΩ ⎞ ⎟ *1 = 0.947 A ⎝ 10.56kΩ ⎠  IL = ⎛⎜  W{ IL  R L = 1KΩ  10kΩ ⎞ ⎟ *1 = 0.909A ⎝ 11kΩ ⎠  IL = ⎛⎜  R L  iS ٪١٠ IL ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ R S ‫א‬  - ١٥٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٢J ٨F  K I L = 750mA ‫א‬ R L ،‫א‬‫א‬‫א‬  A  iL i S = 1A R S = 10kΩ I  RL   B   KE٢J ٨F‫א‬‫א‬‫א‬E٥J ٨F  ‫א‬  W‫א‬،E٣J ٨F‫א‬‫א‬ ⎛ R ⎞ S ⎟⎟iS  I L = ⎜⎜ + R R L⎠ ⎝ S  W‫א‬ iS ، R S ‫א‬  0.75(10 + R L ) = 10 ⇒ 7.5 + 0.75 R L = 10  0.75 R L = 2.5 ⇒ R L = 2.5 = 3.33kΩ 0.75   E٣J ٨F  K‫א‬E٦J ٨F‫א‬‫א‬‫א‬ + R S = 50Ω VS = 100V A    −   KE٣J ٨F‫א‬‫א‬‫א‬E٦J ٨F - ١٥٥ -  B  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    VS 100 = = 2A R S 50  iS =  ‫א‬  W،E٧J ٨F‫א‬‫א‬‫א‬  A i S = 2A  I  R S = 50Ω   B  KE٣J ٨F‫א‬‫א‬‫א‬E٧J ٨F ٣J ٨ ?‫?א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Superposition Theorem ‫א‬   ‫א‬ ‫א‬ ، ‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬ K    ‫א‬‫א‬ ‫א‬‫א‬‫א‬   ‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬،K‫א‬‫א‬ ‫א‬ ، ‫א‬‫א‬‫א‬  K‫א‬‫א‬ ‫א‬  ١J ٣J ٨  ‫א‬‫א‬‫א‬ ‫א‬Superposition Theorem ‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  ٢J ٣J ٨ ‫א‬ ‫א‬‫א‬‫א‬Superposition Theorem‫א‬  W‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬EF‫א‬ K١ - ١٥٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬، ‫א‬‫א‬‫א‬  W‫א‬Open Circuit ‫א‬‫א‬،Short Circuit  A A A Vs A As B B - ١٥٧ - B B      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٢ K‫א‬‫א‬ K٣ K‫א‬‫א‬‫א‬ K٤     K‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ٣J ٣J ٨  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    W‫א‬‫א‬‫א‬ ‫א‬‫א‬ R S ‫א‬‫א‬ ، ‫א‬‫א‬ ♦ ‫א‬‫א‬، R S ‫א‬‫א‬،‫א‬‫א‬ ♦  KShort Circuit‫א‬‫א‬ Open-Circuit‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬،E٨J ٨F‫א‬‫א‬‫א‬ R1 R2 a + + VS1 VS2 R3 − −      b  K‫א‬E٨J ٨F - ١٥٨ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬‫א‬‫א‬E R 3  ‫א‬Fab‫א‬‫א‬‫א‬‫א‬  I 2 ، I1 ‫א‬‫א‬،E٩J ٨F‫א‬ ،‫א‬ab‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ ‫א‬ab‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  K‫א‬ I2 I1 + a a R2 R1 VS1 R3 b + R1 R2 R3   + VS2    b  K‫א‬‫א‬‫א‬E٩J ٨F  EJ ٤J ٨F  K‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬   a + R1 = 100Ω R 3 = 100Ω 10V R 2 = 100Ω − + 5V − b  KEJ ٤J ٨F‫א‬‫א‬‫א‬E١٠J ٨F - ١٥٩ -       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬  WE١١J ٨F10 V‫א‬‫א‬W‫א‬‫א‬‫א‬ a R1 = 100Ω + R 3 = 100Ω 10V R 2 = 100Ω − b  KEJ ٤J ٨F‫א‬‫א‬‫א‬10 V‫א‬‫א‬E١١J ٨F  W‫א‬‫א‬ R 2 ‫א‬ RT = R 2 * R3 100 * 100 + R1 ⇒ RT = + 100 = 150Ω 100 + 100 R 2 + R3 IT = VS 10 = = 66.7mA R T 150  W‫א‬‫א‬ab‫א‬‫א‬‫א‬  Iab = 66.7 * 100 = 33.3mA 100 + 100 WE١٢J ٨F5 V‫א‬‫א‬W‫א‬‫א‬‫א‬  a R1 = 100Ω R 3 = 100Ω R 2 = 100Ω + 5V − b  KEJ ٤J ٨F‫א‬‫א‬‫א‬5 V‫א‬‫א‬E١٢J ٨F - ١٦٠ -      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W R T ‫א‬‫א‬‫א‬ab‫א‬‫א‬‫א‬ RT = R3 +  IT = R1 R 2 100 * 100 ⇒ RT = 100 + = 150Ω 100 + 100 R + R21 VS 5 = = 33.3mA R T 150  Wab‫א‬‫א‬‫א‬ ⎛ R1 I ab = I T ⎜⎜ ⎝ R1 + R 2 ⎞ 100 ⎟⎟ ⇒ I ab = 33.3 * = 16.7 mA 100 + 100 ⎠  W‫א‬‫א‬  ITab = 33.3 + 16.7 = 50mA ، ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  EJ ٤J ٨F  W‫א‬‫א‬‫א‬K R3 ‫א‬‫א‬ I T ‫א‬   Vs1 20v   R1 1KΩ  A  R3 2.2KΩ R2 1KΩ Vs2 15v B - ١٦١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  W VS ‫א‬‫א‬W١‫א‬ 1  VS 2 = o ⇒ ShortCircuit     Vs1 20v   R1 1KΩ  A  Replace Vs2 with a short   R3 2.2KΩ R2 1KΩ   B    W VS ‫א‬ 1  R T = R 1 + (R 2 \ \ R 3 )   RT (S 1 ) = R1 +  ⇒ I I ( S1 ) = R 2 R3 = 1.69kΩ R 2 R3 VS1 20v = = µA RT (S11 ) 1069kΩ  WA,B‫א‬ R2 −3 * I T( S ) 1 R3 R 2 R3 = = 687.5Ω ⇒ I 3( S ) = 3.69mA 1 R 2 + R3  ⇒ I 3(S1 ) =  R 2 −3  - ١٦٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W VS ‫א‬‫א‬W٢‫א‬ 2  VS 1 = o ⇒ ShortCitcuit  Replace Vs1 with a short  Vs1  20v   R1 1KΩ  A  R3 2.2KΩ R2 1KΩ  Vs2 15v    B R3  W‫א‬‫א‬‫א‬‫א‬ C  R1 A   R3 Vs2    W VS ‫א‬ 2  RT = R 2 + (R1 \ \ R3 ) ⇒ RT ( S 2 ) = R 2 +  I T (S2 ) =  I 3( S 2 ) =  R1−3 R1 R3 = 1.69 KΩ R1 + R3 VS 2 = 8.88mA RT (S s ) R1−3 I T ( S1 ) R1 RR = 1 3 = 687.5Ω ⇒ I 3( S 2 ) = 2.78mA R1 + R3 - ١٦٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      W‫א‬‫א‬W٣‫א‬ I 3 = I 3( S1 ) _ I 3( S 2 ) = 3.69mA − 2.78ma ⇒ I 3 = 0.91mA  I 3( S1) ‫א‬‫א‬‫א‬ I   EJ ٤J ٨F  K R2 ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  R2 12Ω   I2 R2 6Ω Vs 36 V Is = 9A      ‫א‬  W، VS ‫א‬ K١ Q Is = o ⇒ Open Circuit  ‫א‬‫א‬ ⇐ R1 I =0 I2(vs) R2 Vs        ‫א‬‫א‬ R2 , R1 ‫א‬   RT = R1 + R 2 ⇒ RT = 12 + 6 = 18Ω V 36 ∴ I 2 (Vs ) = I T = S = = 2A ↓ RT 18 - ١٦٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      W، I S ‫א‬ K٢ QVs = o ⇒ Short Circuit  ‫א‬‫א‬ ⇐  R1=12 Ω  I2 Is = 9A R2 6Ω      K I s ‫א‬‫א‬‫א‬ R2 , R1 ‫א‬  W I 2 ،CDL‫א‬‫א‬  Current Divider Law ⇒ I 2(Is ) = R1,.2 R2 IS R1 * R 2 6Ω * 12Ω = = 4Ω R1 + R 2 6Ω + 12Ω 4Ω = * 9A = 6A ↑ 6Ω  Q R1, 2 =  ∴ I 2(I S )  W‫א‬‫א‬‫א‬‫א‬‫א‬ K٣  W R2 ‫א‬‫א‬‫א‬‫∴א‬  I 2 = I 2( I S ) − I 2(VS ) = 4 A ↑  K I 2(I ) ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ S  E٥J ٨F  KE١٣J ٨F‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬  a + R1 = 220Ω 10V R 2 = 100Ω − A b  KE٥J ٨F‫א‬‫א‬‫א‬E١٣J ٨F - ١٦٥ - i S = 100mA  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  K‫א‬‫א‬‫א‬  KE١٤J ٨F10 V‫א‬‫א‬W‫א‬‫א‬‫א‬ a  R 1 = 220Ω + 10V  R 2 = 100Ω −     b  KE٥J ٨F‫א‬‫א‬‫א‬‫א‬E١٤J ٨F   K‫א‬‫א‬‫א‬‫א‬  W R T ‫א‬‫א‬‫א‬‫א‬ R T = 220 + 100 = 320Ω  iT = i ↓R2 = 10 = 31.2mA 320  31.2mA 10V ‫א‬ R 2 ‫א‬‫א‬‫א‬∴ KE١٥J ٨F100 mA‫א‬‫א‬W‫א‬‫א‬‫א‬  a  R1 = 220Ω R 2 = 100Ω A i S = 100mA    b  KE٥J ٨F‫א‬‫א‬‫א‬‫א‬E١٥J ٨F - ١٦٦ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬ab‫א‬‫א‬ ⎞  i ↓R = iS ⎛⎜ ⎟ 2 220 + 100 220 ⎝ ⎠ ‫א‬ i s ،‫א‬ R 2 ‫א‬‫א‬‫א‬ i ↓ R 2   W‫א‬،‫א‬ ⎛ 220 ⎞ i ↓ R 2 = 100⎜ ⎟ = 68.8mA ⎝ 320 ⎠  ∴ i ↓ R 2 = 68.8mA  K 68.8mA ‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬  W‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬  i = 31.2 + 68.8 = 100mA   Thevenin's Theorem ٤J ٨ ، ‫א‬‫א‬‫א‬‫א‬‫א‬Thevenin's Theorem   ‫א‬ ‫א‬ ‫א‬‫א‬‫א‬    ‫א‬‫א‬‫א‬ KThevenin's EquivalentEF ‫א‬‫א‬ ‫א‬ RTh ‫א‬‫א‬  VTh  ‫א‬‫א‬K‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  R Th ‫א‬‫א‬ VTh   KE١٦J ٨F - ١٦٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    R Th A VTh  r I   B  K??‫א‬E١٦J ٨F ‫א‬‫א‬‫א‬ R Th ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ r ‫א‬‫א‬ I ‫א‬  E٦J ٨F  I = VTh R Th + r  W‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬ ،Open Circuit‫א‬‫א‬‫א‬‫א‬‫א‬ E١  K VTh ‫א‬‫א‬ EZF‫א‬‫א‬‫א‬‫א‬ E٢   F R Th ‫א‬‫א‬‫א‬،Short Circuit‫א‬‫א‬ KE‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R Th   R Th ‫א‬‫א‬ VTh E‫א‬F E٣ ‫א‬  ‫א‬‫א‬ KE١٦J ٨F ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬  I= VTh R Th + r  ‫א‬‫א‬KComplex Circuit‫א‬‫א‬‫א‬   ‫א‬Output‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ - ١٦٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬Open E١  K VTh ‫א‬ ‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫ א‬E٢ K‫א‬‫א‬ R Th  Series Circuit‫א‬‫א‬E‫א‬F E٣ K‫א‬ R L  R Th ، VTh    E٦J ٨F  K‫א‬a،b‫א‬‫א‬‫א‬‫א‬‫א‬ a R 1 = 4Ω + R 2 = 8Ω 10V + 5V R 3 = 6Ω − − b   KE٦J ٨F‫א‬‫א‬‫א‬E١٧J ٨F  ‫א‬ ‫א‬Open‫א‬‫א‬‫א‬ab‫א‬‫א‬W  ‫א‬‫א‬  K VTh ‫א‬b،a‫א‬ a + R 1 = 4Ω R 2 = 8Ω 10V  + 5V − I − b  Kab‫א‬E٦J ٨F‫א‬‫א‬‫א‬E١٨J ٨F - ١٦٩ -     ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W،‫א‬‫א‬‫א‬‫א‬‫א‬ 10 − 5 = I(4 + 8)  ∴I = 10 − 5 5 = A 12 12  W‫א‬‫א‬ Va  ∴ Va = 10 − I * 4 Va = 10 − 5 * 4 = 8.33V 12  ∴ VTh = 8.33V ‫א‬‫א‬‫א‬ a‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ 5V  ‫א‬ ‫א‬a‫א‬  W Va ‫א‬‫א‬ Va = 5 + I * 8 Va = 5 + 8 *8 12  Va = 5 + 3.33 ≈ 8.33V  K‫א‬‫א‬‫א‬ Va ‫א‬‫א‬   R Th = R ab K‫א‬Short R Th W‫א‬‫א‬  KE١٩J ٨F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R 1 = 4Ω R 2 = 8Ω a b  K‫א‬‫א‬E٦J ٨F‫א‬‫א‬‫א‬E١٩J ٨F - ١٧٠ -       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     KE٢٠J ٨F‫א‬‫א‬‫א‬‫א‬ R 1 = 4Ω  R 2 = 8Ω  a  b   KE١٩J ٨F‫א‬‫א‬‫א‬E٢٠J ٨F   WRTh‫א‬ ∴ R Th = R ab = 4*8 = 2.66Ω 4+8  ‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  KE٢١J ٨F  R Th = 2.66Ω  A  VTh = 8.33V 6Ω I   B  KE٦J ٨FE٢١J ٨F   Wab‫א‬‫א‬  I ab = VTh 8.33 = = 0.96A R Th + 6Ω 2.66 + 6 - ١٧١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٧J ٨F  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  K‫א‬  KE٢٢J ٨F، Vs1 ‫א‬‫א‬W‫א‬‫א‬‫א‬ IT1 +  a R 1 = 4Ω R 2 = 8Ω Iab1 R 3 = 6Ω 10V −     b  KE٧J ٨F‫א‬‫א‬‫א‬10 V‫א‬‫א‬E٢٢J ٨F   WIab1‫א‬ RT = 4 + iT 1 = 8*6 = 7.43Ω 8+6 10 8 = 1.345 A ⇒ i ab1 = 1.345 * = 0.77 A 7.43 8+6  KE٢٣J ٨F، Vs 2 ‫א‬‫א‬W‫א‬‫א‬‫א‬ a  IT2 R 1 = 4Ω R 2 = 8Ω Iab2 R 3 = 6Ω  + 5V − b  KE٧J ٨F‫א‬‫א‬‫א‬ 5 V‫א‬‫א‬E٢٣J ٨F - ١٧٢ -       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     WIab2‫א‬ RT = 8 +  iT = 4*6 = 10.4Ω 4+6 5 = 0.48A 10.4  i ab = 0.48 * 4 = 0.192A 4+6 ،‫א‬ab‫א‬‫א‬‫א‬‫א‬‫א‬W ‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬  i ab = 0.77 + 0.192 = 0.962A  K   ‫א‬‫א‬‫א‬‫א‬   E٨J ٨F  W‫א‬E٢٤J ٨F‫א‬‫א‬‫א‬ R L ‫א‬‫א‬‫א‬  K‫א‬EF  KEF a 2mA I   10kΩ    12kΩ   b  KE٨J ٨F‫א‬‫א‬‫א‬E٢٤J ٨F - ١٧٣ - R L = 8kΩ    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ ‫א‬‫א‬12KΩ ، 8KΩ ‫א‬‫א‬‫א‬ ‫א‬‫א‬W   K10KΩ ‫א‬‫א‬ ∴i ↓ = 2 * RL 10 1 2 ⇒ i ↓ = 2 * = mA 10 + 20 3 3 RL  K‫א‬W   KEJ ٢٥J ٨F‫א‬‫א‬ VTh  R L ‫א‬W‫א‬‫א‬  12kΩ a  I=0 2mA 10kΩ I VTh ⇐     b  KRLE٨J ٨F‫א‬‫א‬‫א‬EJ ٢٥J ٨F ∴ VTh = 2mA * 10KΩ = 20V   ‫א‬‫א‬‫א‬W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  KEJ ٢٥J ٨F‫א‬‫א‬‫א‬EF a 12kΩ I=0 10kΩ open b   R Th ⇐  K‫א‬E٨J ٨F‫א‬‫א‬‫א‬EJ ٢٥J ٨F - ١٧٤ -      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     WRTh  ∴ R Th = 10 + 12 = 22KΩ  KE٢٦J ٨FW‫א‬‫א‬  R Th = 22kΩ  A  VTh = 20V R L = 8kΩ I B  KE٨J ٨FE٢٦J ٨F       W‫א‬‫א‬‫א‬ ∴I = I= VTh R TH + R L 2 20 20V = = mA 22 + 8 30KΩ 3  K‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ١J ٤J ٨ ،Bridge Circuit‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬Thevenin's Theorem،‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬،‫א‬  W‫א‬‫א‬،E٢٧J ٨F‫א‬‫א‬  K R L ‫א‬D،COutput‫א‬B،A‫א‬ - ١٧٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬D،C‫א‬‫א‬‫א‬  KSource‫א‬B،A‫א‬  A R2 R1  VS   RL C  D  R3 R4   B  K‫א‬‫א‬E٢٧J ٨F  E٩J ٨F  W‫א‬،E٢٨J ٨F‫א‬‫א‬‫א‬  KD،C‫א‬ R L ‫א‬‫א‬EF  K R L ‫א‬‫א‬‫א‬EF  A R 2 = 680Ω R 3 = 330Ω VS = 24V D R 4 = 560Ω R 3 = 680Ω B  KE٩J ٨F‫א‬‫א‬E٢٨J ٨F - ١٧٦ -   R L = 1kΩ C       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  W‫א‬ ‫א‬‫א‬‫א‬‫א‬D،C‫א‬ R L ‫א‬W‫א‬‫א‬  W VTh D،C VTh = VC − VD  E٧J ٨F    ⎛  R ⎞ ⎛ R ⎞ 3 4 ⎟⎟VS − ⎜⎜ ⎟⎟VS  VTh = ⎜⎜ ⎝ R2 + R4 ⎠ ⎝ R1 + R 3 ⎠ ،K ‫א‬‫א‬ R L ‫א‬‫א‬‫א‬‫א‬‫א‬  WKE٢٩J ٨F  VC = I1R 3 , I1 = VS , R1 + R 3 VD = I 2 R 4 , 24V − VS R2 + R4  I2 I1 + I2 = R 1 = 330Ω R 2 = 680Ω VTh C R 3 = 680Ω VC  D VD R 4 = 560Ω     KRL‫א‬E٩J ٨F‫א‬‫א‬E٢٩J ٨F   WVTh ⎛ 680 ⎞ ⎛ 560 ⎞ ∴ VTh = ⎜ ⎟ * 24 − ⎜ ⎟ * 24 + + 330 680 680 560 ⎝ ⎠ ⎝ ⎠  VTh = 16.158 − 10.838 = 5.32V - ١٧٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     R Th  ‫א‬ ‫א‬‫א‬W‫א‬‫א‬  KE٣٠J ٨F‫א‬‫א‬‫א‬‫א‬D،C‫א‬‫א‬ R1 A C R3 R Th B R2 ⇐ R4 D  KE٩J ٨FRTh‫א‬E٣٠J ٨F  WRTh  E٨J ٨F  RTh =  ∴ R Th = R 1R 3 R 2R 4 + R1 + R 3 R 2 + R 4 330 * 680 680 * 560 + ⇒ R Th = 222.178 + 307.096 = 529.27Ω 330 + 680 680 + 560   KE٣١J ٨FW‫א‬‫א‬  R Th = 529.27Ω  C VTh = 5.32V  R L = 1kΩ I   D  KE٩J ٨FE٣١J ٨F - ١٧٨ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W،‫א‬CD‫א‬‫א‬ ∴ I CD = VTh 5.32 ⇒ I CD = = 3.5mA 529.27 + 1000 RTh + R L  3.5 mACD‫א‬‫א‬‫ ∴א‬  Maximum Power Transfer‫א‬‫א‬ ٢J ٤J ٨ ‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬ RL ‫א‬‫א‬  A  Circuit  RL   B   ‫א‬‫א‬‫א‬E٣٢J ٨F ‫א‬‫א‬Circuit ‫א‬  W‫א‬B , A   Rth  A  VTH  RL    B  ‫א‬‫א‬E٣٣J ٨F - ١٧٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬ ، RTh    ‫א‬‫א‬ R L ‫א‬‫א‬ ‫א‬‫א‬  W‫א‬‫א‬  PL = I 2 T * RL VTh RL : .I T = *V ⇒ PL = RT + RL (RT + RL )2 Th   RL ‫א‬  RL  (RTh + RL ) ‫א‬ ‫א‬‫א‬Power ‫א‬ RL = 2 VTh 2   RTh ‫א‬ RL ‫א‬‫א‬Maximum  RL = RTh ⇒ PLmak EFW    ، ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬  2 PL max = VTh 4 RTh   ‫א‬‫א‬  RTh ‫א‬ RL ‫א‬  W‫א‬ RTh = RL ‫א‬‫א‬‫א‬‫א‬‫א‬،EB, A F R L  RTh A Circ RL B RTh = R L ‫א‬E٣٤J - ١٨٠ - ٨F   RL   VTh B  A   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١٠J ٨F R1=30Ω A  W‫א‬‫א‬‫א‬  I1 IT -  R2 Vs + RL  150Ω 18V  B  E١٠J ٨F‫א‬‫א‬‫א‬E٣٥J ٨F   K (RL ) ‫א‬‫א‬‫א‬‫א‬ RL  K١  PL max ‫א‬‫א‬‫א‬ K٢  ‫א‬ ‫א‬ RL B , A ‫א‬‫א‬W  W RL R1 A   VTh = V AB = V2 =  ∴VTh = 15V  R L ‫א‬‫א‬‫א‬E٣٦J   R2 Vs    B ٨F  W VTh   R2 150Ω VS = * 18 = 15V R1 + R2 180Ω - ١٨١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W RTh W  WShort Circuit‫א‬ VS   R1 A    R2  B   VS  ⇒ RTh = R AB =  ∴ RTh = 25Ω = O ‫א‬‫א‬‫א‬E٣٧J ٨F   R1 * R 2 = 25Ω R1 + R 2  W‫א‬‫א‬W RTh  A   25Ω - RL Vs +  15V B  ‫א‬‫א‬E٣٨J ٨F PL max ‫א‬‫א‬‫א‬  W‫א‬Maximum RL ‫א‬‫א‬‫א‬  R L = RTh = 25Ω  PL max =  2 VTh 15 2 = = 2.25W 4 RTh 4 * 25 - ١٨٢ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W  W‫א‬ K١  W‫א‬‫א‬  -  Vs  +   ‫א‬‫א‬‫א‬E٣٩J ٨F   ‫א‬‫א‬‫א‬‫א‬‫א‬J  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J  ‫א‬ K٢  W‫א‬‫א‬  Is      ‫א‬‫א‬‫א‬E٤٠J ٨F   ‫א‬‫א‬‫א‬‫א‬‫א‬ J E ∞ F‫א‬‫א‬‫א‬‫א‬‫א‬ J - ١٨٣ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬‫א‬‫א‬K٣  W‫א‬‫א‬‫א‬K   J  KE‫א‬F‫א‬‫ א‬J  Open Circuit‫א‬‫א‬‫א‬E٤١J ٨F  W‫א‬‫א‬K  K‫א‬‫א‬–  K‫א‬‫א‬‫א‬J   Short Circuit‫א‬‫א‬‫א‬E٤٢J ٨F E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Mesh Current Analysis  ٥J ٨ ‫א‬‫א‬‫א‬‫א‬ ‫א‬، ‫א‬‫א‬‫א‬  K  ‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬ ،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬MeshK‫א‬‫א‬  K‫א‬b،a‫א‬‫א‬،E٤٣J ٨F‫א‬‫א‬‫א‬ - ١٨٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   R1 a  V1 R3 a  K R2 b d  V2  b   e c R5 R4    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤٣J ٨F   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KMesh‫א‬‫א‬‫א‬‫א‬ K١ K‫א‬‫א‬KCL‫א‬ Meshes ‫א‬‫א‬ K٢ K‫א‬‫א‬‫א‬KVL‫א‬ K٣ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٤ Meshes.‫א‬‫א‬‫א‬‫א‬‫א‬ K٥ K‫א‬‫א‬‫א‬‫א‬‫א‬ K٦  E١٣J ٨F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE١١J ٨F‫א‬ I1 a b I1 c 20Ω  d 10Ω 10V  I3 I2 20Ω 30Ω 20V 10Ω I2 I4 I5 I3 f  KE١١J ٨F‫א‬‫א‬‫א‬E٤٤J ٨F - ١٨٥ - 15V       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K I 5 ، I 4 ، I 3 ، I 2 ، I1 ‫א‬‫א‬‫א‬ I 3 ، I 2 ، I1   EbF‫א‬‫א‬‫א‬ I 5 ، I 4   (a) (b)     I5 = I1 + I2     I 4 = I3 − I 2 ‫א‬‫א‬‫א‬ I 3 ، I 2 ، I1 ‫א‬‫א‬  K‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬ ‫א‬‫א‬  K‫א‬   Mesh E1F‫א‬‫א‬W‫א‬‫א‬     10 = 10I1 + 20I 5  I1 + I2 EaF I 5  (c)    I 2 ، I1  I 5 KW ∴10 = 10I1 + 20I1 + 20I 2  (d)    10 = 30I1 + 20I2  KEdF  (e)  Mesh E2F‫א‬‫א‬W‫א‬‫א‬     20 = 30I2 + 20I5 − 10I4 WEeF I 5 ، I 4 ‫א‬ - ١٨٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    20 = 30I 2 + 20(I1 + I 2 ) − 10(I 3 − I 2 ) 20 = 30I 2 + 20I1 + 20I 2 − 10I 3 − 10I 2 (f) (g)      20 = 20I1 + 60I 2 − 10I3   Mesh E3F‫א‬‫א‬W‫א‬‫א‬     15 = 20I3 + 10I4  WEbF I 4  15 = 20I 3 + 10(I 3 − I 2 ) 15 = 20I 3 + 10I 3 − 10I 2     15 = 30I3 − 10I2 ‫א‬ I 3 ، I 2 ، I1 EhF،EfF،EdF‫א‬ (h)  W‫א‬‫א‬‫א‬ (I)  (II)  (III)      10 = 10I1 + 20I 2 − (0)I3    20 = 20I1 + 60I 2 − 10I3     15 = (0)I1 − 10I2 + 30I3  W(III, II, I)‫א‬  (IV)    ⎡10 ⎤ ⎡30 20 ⎢20⎥ = ⎢20 60 ⎢ ⎥ ⎢ ⎢⎣15 ⎥⎦ ⎢⎣0 − 10 ⎤ − 10⎥ ⎥ 30 ⎥⎦ 0 ⎡I1 ⎤ ⎢I ⎥ ⎢ 2⎥ ⎢⎣I3 ⎥⎦   E٩J ٨F  WEIVF‫א‬‫א‬   [V ] = [R ] ⋅ [I]  W MeshE3F،MeshE2F،MeshE1F  ‫א‬‫א‬‫א‬W [V ] ‫א‬J ‫א‬‫א‬‫א‬F I 3 ، I 2 ، I1 ‫א‬‫א‬  KE - ١٨٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬‫א‬W [R ] ‫א‬J  E١٠J ٨F    ⎡R11 R12 R13 ⎤ [R ] = ⎢⎢R 21 R 22 R 23 ⎥⎥ ⎢⎣R 31 R 32 R 33 ⎥⎦    R 33 ، R 22 ، R11 ‫א‬‫א‬  KMeshE1F‫א‬‫א‬ R11  KMeshE2F‫א‬‫א‬ R 22  KMeshE3F‫א‬‫א‬ R 33   R12   ‫א‬‫א‬‫א‬‫א‬  KMeshE2F،MeshE1F‫א‬‫א‬  K‫א‬MeshE3F‫א‬،MeshE2F‫א‬‫א‬‫א‬ R 23 ‫א‬ ‫א‬‫א‬MeshE3F‫א‬MeshE1F‫א‬  K‫א‬R13 ‫א‬‫א‬‫א‬‫א‬  K I 3 ، I 2 ، I1  ‫א‬‫א‬‫א‬  ‫א‬E١ R 11  E١١J ٨F   R 12 R 13   ∆ = R 21 R 22 R 23 R 31 R 32 R 33  K‫א‬∆  W‫א‬‫א‬‫א‬  ∆ = R11{R 22 R 33 − R 32 R 23} − R12 {R 21R 33 − R 31R 23} + R13 {R 21R 32 − R 31R 22 }  ‫א‬‫א‬‫א‬  W I1 ‫א‬ - ١٨٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    E١٢J ٨F   V1 R12 R13 1 V2 R 22 R 23 I1 = ∆ V3 R 32 R 33  W I 2 ‫א‬  E١٣J ٨F   R11 1 R 21 I2 = ∆ R 31 V1 R13 V2 R 23 V3 R 33  W I 3 ‫א‬  E١٤J ٨F   R11 1 R 21 I3 = ∆ R 31 R12 V1 R 22 V2 R 32 V3  ‫א‬ I 3 ، I 2 ، I1 ‫א‬ ∆ ‫א‬‫א‬  W‫א‬  ∆ ‫א‬  30 ∆ = 20 20 0 60 − 10 0 − 10 30 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ∆ = 30(60 * 30 − 10 * 10 ) − 20(20 * 30 − 0 ) + 0(KK) ≈ 39000   W‫א‬، I1   10 20 0 1 I1 = 20 60 − 10 ∆ 15 − 10 30  W‫א‬ ∴ I1 = 1 {10(60 * 30 − 100) − 20(20 * 30 + 15 * 10)} ≈ 0.05128A 39000 - ١٨٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W 30 10 0 30 10 0 1 1  I 2 = 20 20 − 10 = ⋅ 20 20 − 10 39000 ∆ 0 15 30 0 15 30  ‫א‬‫א‬‫א‬  I2 = 0.423A  W 30 20 10 1  I3 = 20 60 20 ∆ 0 − 10 15  ‫א‬ ∆ ‫א‬‫א‬‫א‬  I3 = 0.641A   I 5 ، I 4  I 3 ، I 2 ، I1 ‫א‬‫א‬‫א‬‫א‬ I 4 = I 3 − I 2 = 0.218A I 5 = I1 + I 2 = 0.05128 + 0.42300 = 0.47428A    ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  - ١٩٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     'Summary'‫א‬  K‫א‬‫א‬‫א‬‫א‬ KCL  E١F ‫א‬‫א‬ KVL  E٢F  K‫א‬  K E٣F  K‫א‬‫א‬‫א‬‫ א‬E٤F  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٥F ‫א‬‫א‬‫א‬‫א‬ ‫א‬ E٦F ،‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٧F  K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٨F K‫א‬‫א‬‫א‬‫א‬ R Th ‫א‬‫א‬ VTh        - ١٩١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬   K R S = 50Ω ، VS = 300V E١F  K‫א‬‫א‬‫א‬‫א‬‫א‬E٢F   2 .2 Ω 100Ω 5kV 12V      K R S = 1.2KΩ ، iS = 600mA ‫א‬‫א‬E٣F   K‫א‬‫א‬‫א‬‫א‬E٤F  0.01A 2.7 kΩ I 10mA I  4.7 kΩ     K‫א‬‫א‬‫א‬ R 5 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥F R1 = 1kΩ 2V  R 3 = 1kΩ  R 2 = 2.2kΩ R 4 = 1kΩ  R5   3V - ١٩٢ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬ R 3 ‫א‬‫א‬‫א‬‫א‬‫א‬E٦F R 3 = 330Ω  R 1 = 680Ω 100mA  R 2 = 220Ω R 4 = 470Ω I 20V      K R L ‫א‬‫א‬‫א‬‫א‬ E٧F  40V 8.2kΩ 1kΩ  560Ω  R 5 = 1.5kΩ I 0 .5 A  60V 1kΩ    ‫א‬‫א‬ R L ‫א‬‫א‬‫א‬E٨F A R 2 = 820Ω R 1 = 1kΩ R L = 1kΩ VS = 12V C D R 3 = 2.2kΩ R 4 = 1.2kΩ B - ١٩٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬A, B‫א‬E٩   R 1 = 10Ω R 2 = 15kΩ +   10V A −  B R 3 = 12kΩ  R4 I = 0.2mA     W‫א‬‫א‬‫א‬B , A ‫א‬‫א‬‫א‬‫א‬‫א‬E١٠F  R1  22Ω 100Ω  78Ω Vs 25V      KB , A ‫א‬‫א‬،‫א‬‫א‬‫א‬E١١F  A R1  4Ω  - Vs + 20V   - ١٩٤ - R3=4Ω Is 2A R2 8Ω B   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     K‫א‬‫א‬‫א‬KB , A ‫א‬‫א‬،‫א‬‫א‬‫א‬E١٢F  R3=10Ω R1 20Ω    Vs 24V  Ru=50Ω R2    120Ω   W‫א‬‫א‬E١٣F  K‫א‬‫א‬‫א‬ RL ‫א‬ K١ K‫א‬‫א‬‫א‬ K٢ R1 Vs 18V 3Ω R3 R2 2Ω   A RL 6Ω B      - ١٩٥ -  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ٩  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٤ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬  W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   - ١٩٥ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬ Introduction١J ٩ ‫א‬،Resistor‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬،Inductor‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬،Capacitor  K‫א‬‫א‬‫א‬  Capacitor Characteristics ‫א‬‫א‬٢J ٩  Basic Structure‫א‬١J ٢J ٩ EF  ‫א‬   KE١J ٩F،Dielectric ‫א‬  ‫א‬E١J ٩F    K‫א‬‫א‬‫א‬ How Capacitors Store charges‫א‬ ٢J ٢J ٩   ‫א‬‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  W‫א‬‫א‬‫א‬، - ١٩٦ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬ e e e e e e e e e e A      B ‫א‬  ‫א‬‫א‬E٢J ٩F    A‫א‬‫א‬‫א‬، ‫א‬ ‫א‬‫א‬  B‫א‬‫א‬‫א‬  K    K‫א‬‫א‬‫ א‬K١ W‫א‬‫א‬KDielectric‫א‬‫א‬ K٢ + - + - + - + -   e e e e - + e A B e e e e e   V s  ‫א‬‫א‬‫א‬E٣J ٩F - ١٩٧ -       ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬ B‫א‬‫א‬A‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬K‫א‬ ‫א‬‫א‬K ‫א‬‫א‬، VS ‫א‬  K‫א‬‫א‬‫א‬    K ‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬  Q Q + _ + _ + _ + _ + _ A       B  d  ‫א‬‫א‬‫א‬‫א‬‫א‬E٤J ٩F   ‫א‬‫א‬،  ‫א‬ ‫א‬  ‫א‬  W= 1 CV 2  2  W‫א‬‫א‬‫א‬‫א‬‫א‬           E١J ٩F  - ١٩٨ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬ Capacitance‫ א‬٣-٢-٩ ‫א‬‫א‬‫א‬ ‫א‬‫א‬Capacitance ‫א‬  ‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬ K1V   ،V  ‫א‬،‫א‬،‫א‬  W‫א‬،Q Q V  C=  Q = C.V  V=     EJ ٢J ٩F    EJ ٢J ٩F Q  C  E٣J ٩F  W  K‫א‬‫א‬C  K‫א‬Q  K‫א‬V   KFarad‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ 1C 1Farad   K1V      W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   1µF = 10 −6 F 1nF = 10 −9 F 1 pF = 10 −12 F  E١J ٩F ‫א‬‫א‬‫א‬K  10V  ‫א‬، 50µC   C= Q 50µC = = 5µF V 10V - ١٩٩ -  W  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  Voltage Rating‫א‬‫א‬‫א‬‫ א‬٤-٢-٩ ، ‫א‬،  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬KVoltage Rating‫א‬‫א‬ K  ‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  Temperature Coefficient‫א‬‫א‬‫ א‬٥-٢-٩  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬KTemperature Coefficient‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬K ‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ ( parts millian) C o   K ppm Co     E٤J ٩F W‫א‬‫א‬‫א‬   E٢J ٩F  K − 150 ppm \ C o ‫א‬‫א‬1µF ‫א‬‫א‬  ‫א‬  K‫א‬‫א‬‫א‬‫א‬ ⇐ ‫א‬ ١٥٠ ‫א‬  ‫א‬    ‫ ⇐ א‬1C o ‫א‬  W،‫א‬‫א‬  150 150 * 1µF = 6 * 10 − 6 F = 150 * 10 −12 F = 150 pF 1000000 10   ‫א‬  150 pF ‫א‬ ‫א‬‫א‬ ⇐ 1C o ‫א‬  K1µF − 150 pF  - ٢٠٠ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬ Dielectric Strength‫א‬ ٦-٢-٩  ‫א‬K   ‫א‬‫א‬‫א‬   W‫א‬‫א‬  Volt mil lim eter ‫א‬ 1000V \ mm ‫א‬‫א‬،‫א‬K V \ mm ‫א‬‫א‬  K 1000V ‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬   ‫א‬‫א‬  WE‫א‬‫א‬F ‫א‬‫א‬،Paraffin paper‫א‬،Teflon‫א‬،Mica‫א‬،Glass‫א‬  KAir‫א‬‫א‬،Oil‫א‬،Ceramic   Leakage‫ א‬٧-٢-٩ KIdeal Dielectric،‫א‬‫א‬ ‫א‬  ، ‫א‬‫א‬  ‫א‬ ‫א‬،‫א‬Dielectric   ‫א‬‫א‬‫א‬K  ‫א‬  W‫א‬   R leakage     E‫א‬F‫א‬‫א‬E٥J ٩F    K‫א‬‫א‬ R Leakage W  - ٢٠١ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  Physical Characteristics of Capacitors‫א‬‫ א‬‫א‬ ٨-٢-٩  W،‫א‬‫א‬  Plate Area‫א‬ K١ K‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Plate Separation‫א‬‫א‬‫ א‬K٢ K  ‫א‬  ‫א‬ ‫א‬‫א‬‫א‬ ‫א‬ ‫א‬، ‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬        d  ‫א‬‫א‬E٦J ٩F        d  ‫א‬‫א‬E٧J ٩F - ٢٠٢ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  Dielectric Constant ε r ‫א‬ K٣ ‫א‬،‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬  W ‫א‬‫א‬W  K V0 { ‫א‬‫א‬‫א‬‫א‬‫א‬} ‫א‬،EFW  W، V ‫א‬‫א‬‫א‬  V < Vo  KC‫א‬‫א‬‫א‬، C = Q ‫א‬W V   δ ‫א‬‫א‬‫א‬‫א‬Dielectric Constant‫א‬  W‫א‬‫א‬ECF‫א‬  εr = C Co        E٥J ٩F  K‫א‬CW  K‫א‬ Co   W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  ‫א‬  Dielectric Material  Air (Vacuum) E‫א‬‫א‬F‫א‬‫א‬    Dielectric Constant Teflon  paper ( paraffin)   ε r ‫א‬ Oil ‫א‬  Mica ‫א‬  Glass ‫א‬  1  2 2 .5   Ceramic ‫א‬‫א‬  4 5 7 .5  1200  ‫א‬‫א‬‫א‬E١J ٩F - ٢٠٣ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  W‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  C= ( A * ε r * 8.85 * 10 −12 d )     E٦J ٩F  K m 2 ‫א‬ PlateArea ‫א‬‫א‬ A W  K m ‫א‬‫א‬‫א‬ d   K‫א‬ ε r   K F / m ،Vacuum Permittivity‫א‬‫א‬ 8.85 * 10 −12 ‫א‬‫א‬   E٣J ٩F K d = 8mm  ‫א‬، A = 0.04m 2 Mica ‫א‬  K‫א‬‫א‬  ‫א‬  2 0.04m * 5 * 8.85 * 10 −12 = 2.2 * 10 −10 F = 2.2 * 10 2 * 10 −12 F 0.008m ⇒ C = 220 pF C=   Types of Capacitors ‫א‬‫א‬٣J ٩  W،‫א‬  Fixed Capacitors‫א‬‫ א‬١-٣-٩  W،‫א‬‫א‬  Mica Capacitors‫א‬ K١ ،‫א‬‫א‬،  ‫א‬‫א‬‫א‬ ‫א‬‫א‬K ،‫א‬  W‫א‬، - ٢٠٤ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬   ‫א‬E٨J ٩F  Voltage E  ‫א‬F‫א‬‫א‬، 0.1µF → 1 pF ‫א‬‫א‬‫א‬‫א‬  K − 20 ppm / C o → 100 ppm / C o ‫א‬‫א‬‫א‬،1000V → 2500V ‫א‬Rating ‫א‬، ε r  Ceramic Capacitor‫א‬‫א‬ K٢  ‫א‬ ‫א‬  ‫א‬‫א‬ = 1200  ‫א‬، 1 pF → 2.2µF ‫א‬‫א‬، ‫א‬‫א‬، 200000 ppm\ oC ‫א‬   ‫א‬‫א‬‫א‬، 6000V ‫א‬  K‫א‬‫א‬   E٤J ٩F ‫א‬  ‫א‬ 1o C ‫א‬ ‫א‬‫א‬‫א‬،1µF   K 0.2µF ‫א‬، 200000 * 1µF 1000000  Plastic Film Capacitor‫א‬‫ א‬K٣  W،‫א‬‫א‬‫א‬‫א‬  Poly Carbonate‫א‬ J   Propylene‫ א‬J     Polyester‫ א‬J  100µF ‫א‬  - ٢٠٥ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  Electrolytic Capacitors‫א‬‫ א‬K٤ K‫א‬‫א‬‫א‬   ‫א‬EF‫א‬ ‫א‬، 200000µF ، ‫א‬‫א‬ ‫א‬K  ‫א‬‫א‬‫א‬  ، 350V  ، ‫א‬  K‫א‬   Variable Capacitors‫א‬‫ א‬٢-٣-٩  W‫א‬‫א‬K‫א‬‫א‬      ‫א‬‫א‬‫א‬E٩J ٩F  W  Air Capacitor‫א‬‫א‬‫ א‬K١ ‫א‬،‫א‬‫א‬‫א‬‫א‬  ‫א‬K ‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬  Trimmers‫א‬ K٢  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Varactors ‫א‬‫א‬ K٣  K‫א‬‫א‬ - ٢٠٦ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  Connection Types of Capacitors ‫א‬‫א‬٤J ٩  ‫א‬‫א‬ Series‫א‬‫א‬، ‫א‬ Series – Parallel‫א‬J   ‫א‬Parallel‫א‬‫א‬  W‫א‬‫א‬   Series Capacitors‫א‬‫א‬ ١-٤-٩    C1 C N  C2   V1  V2  VN   ‫א‬‫א‬‫א‬E١٠J ٩F   ‫א‬‫א‬،EF‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬EF‫א‬B,A V S = V1 + V2 + ...... + V N       E٧J ٩F   W‫א‬‫א‬‫א‬‫א‬W  CT = 1 1 1 1 + + .... C1 C 2 CN  W‫א‬‫א‬‫א‬‫א‬        E٨J ٩F  W  W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K١ K‫א‬‫א‬‫א‬‫א‬ K٢ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٣  W‫א‬‫א‬ - ٢٠٧ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬   ١١١  ‫א‬  ‫א‬  ‫א‬ C1  C 2    ‫א‬‫א‬E١١Z٩F  W‫א‬‫א‬‫א‬،‫א‬‫א‬ CT ‫א‬‫ א‬K١ CT = C1C 2 C1 + C 2       E٩J ٩F  W‫א‬‫א‬،C‫א‬‫א‬‫א‬ K٢  CT = C N      E١٠J ٩F  E٥J ٩F  C1 = 10µF , C1 = 3µF , C1 = 8µF ،‫א‬  K CT ‫א‬‫א‬،‫א‬‫א‬  CT = 1 1 = = 2.35µF 1 1 1 1 1 1 + + + + C1 C 2 C 3 10 * 10 − 6 5 * 10 − 6 8 * 10 − 6  ‫א‬   Parallel Capacitors‫א‬‫א‬ ٢-٤-٩ ‫א‬،EF‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬KEFA,B‫א‬‫א‬  I T = I c1 + I C 2 + ....I CN    - ٢٠٨ -   ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬   C1     A C2 CN  B   ‫א‬‫א‬‫א‬E١٢J ٩F  ‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬   CT = C1 + C 2 + ..... + C N   W‫א‬E‫א‬F     E١١J ٩F    W،C‫א‬‫א‬‫א‬ CT = N * C       E١٢J ٩F  E٦J ٩F  W‫א‬‫א‬‫א‬، CT ‫א‬‫א‬   1µF 2µF   3µF    ‫א‬ CT = 1µF + +2 µF + 3µF = 6 µF  - ٢٠٩ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  Charging & Discharging of Capacitors ‫א‬٥J ٩   ‫א‬K‫א‬DC‫א‬‫א‬  W،  Charging Capacitors‫א‬ ١-٥-٩  W‫א‬‫א‬‫א‬‫א‬ C + + +  _  VR  I _   R  -  +   ‫א‬‫א‬E١٣J ٩F  W‫א‬‫א‬،  VS ‫א‬‫א‬، VC   = VC + V R ‫א‬‫א‬ = 0 ‫א‬‫א‬‫א‬‫א‬  K XC = 0Ω  K١ V S = VC + V R ، V R = V S W،‫א‬ V R  ⇐  I= VR Vs = R R   R ‫א‬‫א‬‫⇐ א‬ ‫א‬Short Circuit ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬K X C = 0 ‫א‬    Vc   ‫א‬،‫א‬ K٢ K VS ‫א‬ VR + VC ‫א‬ VR ‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬،،   I = VR ‫א‬ ⇐ R  K OpenCircuit ‫א‬‫א‬‫א‬ - ٢١٠ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬   VC = VS ‫א‬ VC ‫א‬‫א‬ ، X C = ∞ ‫א‬‫א‬‫א‬  K٣   ‫א‬    ‫א‬‫א‬ ‫א‬‫א‬K‫א‬ ‫א‬   V R = 0 ،‫א‬  K‫א‬‫א‬‫א‬‫א‬     ‫א‬ ‫א‬،Open Circuit‫א‬‫א‬  K  Discharging Capacitors‫א‬ ٢-٥-٩  W‫א‬‫א‬‫א‬،‫א‬  C I  _ VC   I  R  VR  ‫א‬‫א‬E١٤J ٩F   _ + + +    VC = VR W     K‫א‬‫א‬‫א‬‫א‬  - ٢١١ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬ K١  K I = VR ‫א‬‫א‬ R WK‫א‬ VR  VC ‫א‬،‫א‬ K٢ ↓ I ⇐  ↓ V R , ↓ VC   ،‫א‬‫א‬ ‫א‬‫א‬ K٣  K I = 0 ‫א‬  RC Time Constant‫א‬ ٣-٥-٩ ‫א‬‫א‬،‫א‬‫א‬‫א‬    W،Time Constant‫א‬‫א‬ τ = R *C  W T: second R: ohm C: farad  W ‫א‬‫א‬، 63%   ‫א‬‫א‬‫א‬  ‫א‬‫א‬W τ ‫א‬‫א‬‫א‬ τ ‫א‬،K‫א‬‫א‬ 63% ‫א‬  K‫א‬‫א‬ 63% Charging and Discharging Curves ‫א‬‫א‬٤J ٥J ٩  ،‫א‬  W‫א‬‫א‬‫א‬‫א‬KExponential Curve‫א‬  ⎡ t⎤ V = V F + (V I − V F ) * exp ⎢− ⎥  ⎣ τ⎦     E١٣J ٩F  Exponential Function‫א‬‫א‬ exp W - ٢١٢ -      ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  W‫א‬‫א‬‫א‬   ‫א‬‫א‬E١٥J ٩F  W  K‫א‬‫א‬‫א‬ K١ W‫א‬ K٢  K‫א‬‫א‬‫א‬‫א‬ Vi  K‫א‬‫א‬‫א‬ VF  VF > Vi W W‫א‬ K٣  K‫א‬‫א‬‫א‬‫א‬ Vi  K‫א‬‫א‬‫א‬ VF  V F < Vi W W‫א‬ K٤  Charging from Zero‫א‬‫א‬ K ، Vi = 0 ، ‫א‬‫א‬‫א‬  ‫א‬‫א‬  W‫א‬‫א‬‫א‬ ⎛ ⎡ t ⎤⎞ V = V F ⎜⎜1 − exp ⎢− ⎥ ⎟⎟  ⎣ τ ⎦⎠ ⎝      E١٤J ٩F  Discharging to Zero‫א‬‫א‬ ‫א‬‫א‬‫א‬  ، V F  ⎛ ⎡ t ⎤⎞ V = Vi ⎜⎜1 − exp ⎢− ⎥ ⎟⎟  ⎣ τ ⎦⎠ ⎝     - ٢١٣ - = 0 ‫א‬‫א‬ K   W      E١٥J ٩F  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  E٧J ٩F  W‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  R=8.2kΩ C=0.01µF 50V  E٧J ٩F‫א‬‫א‬‫א‬E١٦J ٩F      ‫؟‬‫א‬‫א‬ 50µs ‫א‬‫א‬  ‫א‬   Qτ = R.C = 82µs ⎛ ⎡ 50 µs ⎤ ⎞ ⎛ ⎡ t ⎤⎞ QVC = V F ⎜⎜1 − exp ⎢− ⎥ ⎟⎟ ⇒ VC = 50⎜⎜1 − exp ⎢− ⎥ ⎟⎟ = 22.8V s τ µ 82 ⎣ ⎦ ⎝ ⎠ ⎣ ⎦⎠ ⎝  VC = 22.8V ‫א‬‫א‬ 50µs    E٨J ٩F  W‫א‬‫א‬‫א‬  10V  + - R=10k C=2µF    E٨J ٩F‫א‬‫א‬‫א‬E١٧J ٩F   ‫؟‬ 6ms ‫א‬‫א‬  τ = R.C = 10 * 10 3 * 2 * 10 −6 = 20ms  ⎡ VC = Vi * exp ⎢− ⎣  W‫א‬‫א‬، t = 6ms  t⎤ ⎡ 6ms ⎤ = 10V * exp ⎢− ⎥ ⎥ = 7.41V z⎦ ⎣ 20ms ⎦  - ٢١٤ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬  ‫א‬‫א‬  W‫א‬W  K‫א‬‫א‬ K K‫א‬‫ א‬K   W‫א‬W  K V = 10V  Q = 50µC ‫א‬،Capacitance‫א‬ K١ K Q = 2mC ، C = 200µF Capacitance‫א‬‫א‬،Voltage‫א‬ K٢ ‫א‬ 0.0008m ‫א‬ A = 0.001m 2 ‫א‬‫א‬Mica K٣ ‫؟‬‫א‬ ‫א‬، − 200 ppm \ o C ‫א‬‫א‬ 25 o C ‫א‬‫א‬ 1000 pF  K٤ ‫ ؟‬75 o C ‫א‬‫א‬ W‫א‬‫א‬ K٥ C1= 100 pf    100 v C2= 500pf     C3= 400 pf    100 v 5µ 3µ 2µ    - ٢١٥ -  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬   10µ  2µ 5µ  3µ   100 µ  500µ   5v  1000µ  100 µ 200µ   500µ  W‫א‬‫א‬‫א‬ K٦  (a )10µs(b )20µs(c )30µs(d )40µs   R= 10 k   C=0.001µF V      - ٢١٦ -   ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬ W‫א‬‫א‬، 25V ‫א‬ K٧ (a) 1.5ms (b) 4.5ms (c) 6ms (d) 7.5ms   25 v ++++ ------+  C=1.5µf   - ٢١٧ - R= 1 k  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ١٠  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٤ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬ W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٢١٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction١J ١٠ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬،Inductor‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬   Inductance Characteristics E‫א‬F‫א‬‫א‬٢J ١٠  Basic Structure‫א‬١J ٢J ١٠ ،‫א‬‫א‬‫א‬  ،‫א‬‫א‬K ‫א‬  KE١J ١٠F  ‫ﻣﺠﺎل‬ ‫ﻣﻐﻨﺎﻃﻴﺴﻲ‬    ‫ﺑﻄﺎرﻳﺔ‬   ‫א‬‫א‬‫א‬‫א‬‫א‬E١J ١٠F   ‫א‬‫א‬، ‫א‬‫א‬‫א‬   ‫א‬‫א‬K ‫א‬  ‫א‬‫א‬  KFaraday ‫א‬‫א‬KInduced‫א‬ Voltmeter‫א‬E‫א‬F‫א‬‫א‬‫א‬ E  ‫א‬F‫א‬ ‫א‬‫א‬‫א‬‫א‬K  ‫א‬  W‫א‬‫א‬ S  N  Voltmeter ‫ﻣﻐﻨﺎﻃﻴﺲ‬  ‫א‬E٢J ١٠F - ٢١٩ -    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W  K‫א‬‫א‬‫א‬‫א‬‫א‬ K١ KInductance‫א‬‫א‬‫א‬ K٢  Inductance ‫ اﻟﻤﺤﺎﺛﺔ‬٢-٢-١٠ ‫א‬‫א‬‫א‬Inductance‫א‬ ‫א‬KHHenry ‫א‬K‫א‬‫א‬‫א‬  W،‫א‬‫א‬  mH = 10 −3 H µH = 10 −6 H  W‫א‬،‫א‬‫א‬    ‫א‬‫א‬E٣J ١٠F  ١F، 1A / sec ‫א‬‫א‬‫א‬‫א‬ 1H  ‫א‬،‫א‬‫א‬ 1V  ‫א‬ ،E‫א‬  K1H ‫א‬ How Inductors Store charges‫א‬  ٣-٢-١٠  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬  W=  W‫א‬‫א‬‫א‬ 1 * LI 2  2   E١J ١٠F  W  KJoule‫א‬W  KHenry‫א‬L  KAmpere‫א‬A - ٢٢٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٢J ١٠  Formula of Inductance in terms of its Physical Characteristics ‫א‬‫א‬،Core‫א‬ ‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬  KCobalt ‫א‬،Iron‫א‬Ferromagnetic PermeabilityE‫א‬F‫ א‬١-٤-٢-١٠  ‫א‬‫א‬W   ‫א‬‫א‬   ‫א‬‫א‬‫א‬ K ‫א‬‫א‬Permeability  K µ   ‫א‬‫א‬‫ א‬٢-٤-٢-١٠  ،A‫א‬‫א‬،N‫א‬‫א‬‫א‬‫א‬    W‫א‬‫א‬، µ ‫א‬، l ‫א‬   ‫א‬‫א‬‫א‬E٣J ١٠F  ‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬،  L= N2 *µ* A  l  W   E٢J ١٠F    F‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  KE‫א‬‫א‬ - ٢٢١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١J ١٠F  WInductance‫א‬،‫א‬‫א‬   E١J ١٠F‫א‬‫א‬E٤J ١٠F   L=  µ = o.25 * 10 −3 ‫א‬‫א‬‫א‬ N 2 µ . A 4 2 * 0.25 * 10 −3 * 0.1 = = 40mH e 0.01  ‫א‬ Winding Resistance and Capacitance‫א‬‫א‬٥J ٢J ١٠  ‫א‬K ‫א‬‫א‬، ‫א‬  ‫א‬K ‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬، RW Winding Resistance‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K    ‫א‬‫א‬‫א‬،  WEF   ‫א‬‫א‬‫א‬E٥J ١٠F  ‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬،‫א‬،‫א‬KWinding Capacitance CW - ٢٢٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬K ‫א‬‫א‬‫א‬K  W‫א‬‫א‬‫א‬،‫א‬‫א‬،‫א‬  CW     R L   ‫א‬‫א‬‫א‬E٦J ١٠F   Inductors TypesE‫א‬F‫א‬‫א‬٣J ١٠  W‫א‬E‫א‬F‫א‬   KFixed Inductors‫א‬ K١  KVariable Inductors‫א‬ K٢  W‫א‬‫א‬ W‫א‬،Air- Core‫א‬‫א‬‫א‬ K١ ‫א‬‫א‬‫א‬E٧J ١٠F  W‫א‬،Ferrite - Core‫א‬‫א‬ K٢ ‫א‬‫א‬E٨J ١٠F W‫א‬،Iron - Core‫א‬‫א‬ K٣  ‫א‬‫א‬E٩J ١٠F - ٢٢٣ -      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Connection Types of Inductors‫א‬‫א‬ Capacitors‫א‬Resistors‫א‬Inductors‫א‬ ٤J ١٠  W  Series Inductors‫א‬‫א‬‫א‬١J ٤J ١٠  L2 ‫א‬‫א‬‫א‬ L1 ‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ L1 L2  Ln    ‫א‬‫א‬‫א‬E١٠J ١٠F   W‫א‬‫א‬‫א‬‫א‬‫א‬ LT ‫א‬‫א‬  LT = L1 + L2 + .... + L N    E٣J ١٠F  Parallel Inductors‫א‬‫א‬‫א‬٢J ٤J ١٠  ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  W‫א‬   L1 L2  Ln  ‫א‬‫א‬‫א‬E١١J ١٠F - ٢٢٤ -       ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    LT =   W‫א‬ LT ‫א‬‫א‬ 1 1 1 1 + + ... + L1 L2 LN    E٤J ١٠F     K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   Inductors in DC Circuits‫א‬‫א‬‫א‬‫ א‬٥J ١٠ ‫א‬‫א‬‫א‬‫א‬ E‫א‬F‫א‬ ‫א‬  ‫א‬‫א‬  K،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ KOpen Circuit‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬K ‫א‬‫א‬  W،‫א‬‫א‬ I   I It    t    ‫א‬‫א‬E١٢J ١٠F - ٢٢٥ - t   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W ،Short Circuit‫א‬‫א‬‫א‬‫א‬ K١  K‫א‬ ‫א‬  K‫א‬ K٢  K - ٢٢٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Summary ‫א‬ K‫א‬‫א‬‫א‬ K١ ‫א‬‫א‬‫א‬Inductance‫ א‬K٢ KHHenry ‫א‬K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F‫ א‬K٣  W= 1 * LI 2 2  W‫א‬‫א‬‫א‬  W‫א‬‫א‬E‫א‬F‫א‬Formula‫א‬‫ א‬K٤ L= N2 *µ* A l Capacitors‫א‬Resistors‫א‬Inductors‫א‬ K٥ W LT = L1 + L2 + .... + L N  LT = 1 1 1 1 + + ... + L1 L2 LN ‫א‬ • ‫א‬ • ‫א‬‫א‬‫א‬،‫א‬‫א‬E‫א‬F‫ א‬K٦ ‫א‬،Open Circuit‫א‬ K‫א‬ - ٢٢٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬  K‫א‬‫א‬ K١ ‫؟‬‫א‬،‫א‬‫א‬ K٢ ‫؟‬‫א‬،‫א‬‫א‬ K٣ ‫א‬K A = 10 *10 −5 m 2 ‫א‬  L = 0.05m  (Core) K٤ ‫א‬‫א‬‫א‬  ‫א‬K µ = 1.2 * 10 −6 ‫א‬ ‫ ؟‬L = 30mH ‫א‬ W‫א‬،‫א‬‫א‬‫א‬ K٥   L1 = 3H , L2 = 5H , L N = 2 H L1  L2 Ln    K LT ‫א‬‫א‬ W‫א‬،‫א‬‫א‬‫א‬ K٦   L1 = 3H , L2 = 6 H , L N = 2 H   L1 L2 Ln   K LT ‫א‬‫א‬ - ٢٢٨ -   ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ١١  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٦ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬  W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   - ٢٣٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction١J ١١ ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ KEDCF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬،EACFAlternating Current ‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬ ‫א‬ESinusoidal F‫א‬‫אא‬‫א‬‫א‬‫א‬  KSine wave ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  K Magnetic Effects of Electrical Current ‫א‬‫א‬‫א‬٢J ١١ Generation & Concentration of Magnetic Field‫א‬‫א‬١J ٢J ١١ ‫א‬‫א‬‫א‬، ‫א‬‫א‬ ‫א‬F‫א‬‫א‬‫א‬(Magnetic Field)‫א‬  ‫א‬‫א‬‫א‬،Eφ،E  ‫א‬‫א‬F‫א‬  KE١J ١١F I ϕ  K‫א‬‫א‬‫א‬E١J ١١F - ٢٣١ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬W  ‫א‬‫א‬ K‫א‬  W ‫א‬‫א‬‫א‬‫א‬ K١  KE٢J ١١F  ϕ1  K‫א‬‫א‬‫א‬E٢J ١١F    ‫א‬، ‫א‬EφF‫א‬‫א‬ K٢ ،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬ ‫א‬،E  F‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬  A B  K‫א‬‫א‬‫א‬‫א‬E٣J ١١F ‫א‬‫א‬، ‫א‬‫א‬‫א‬ E  ‫א‬‫א‬F‫א‬  ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٢٣٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬Eφ1F‫א‬‫א‬(φ2)‫א‬‫א‬‫א‬  KE٣J ١١F‫א‬ ‫א‬،‫א‬‫א‬‫א‬  KE٤J ١١F‫א‬‫א‬‫א‬‫א‬ ϕ  KE٤J ١١F  ϕ1<ϕ2<ϕ3        W  E١J ١١F ‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  Basic Concepts of Electrical Generator‫א‬‫א‬٣J ١١ ‫א‬‫א‬‫א‬‫א‬،E٤J ١١F  ‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،  KE٥J ١١F،‫א‬ - ٢٣٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     N S  K‫א‬‫א‬‫א‬‫א‬‫א‬E٥J ١١F  ‫א‬W  ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬   Generation of Sine Wave‫א‬‫א‬١J ٣J ١١ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،E٦J ١١F،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬EF N B C ω A x D φ S  K‫א‬‫א‬E٦J ١١F - ٢٣٤ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    BA‫א‬‫א‬،E٦J ١١F‫א‬‫א‬‫א‬  W‫א‬،ADC ‫א‬‫א‬‫א‬A‫א‬ E١F ‫א‬‫א‬‫א‬‫א‬B‫א‬ E٢F  K‫א‬ ‫א‬‫א‬E  ‫א‬‫א‬F ‫א‬ KE٦J ١١F‫א‬ K‫א‬‫א‬‫א‬‫א‬C‫א‬ ‫א‬‫א‬  ‫א‬‫א‬D‫א‬ E٣F (٤)  ‫א‬‫א‬‫א‬E  ‫א‬‫א‬F‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ K‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬   L KE٧J ١١F 1 0.5 0 -0.5 -1 0 90 180 270 360 ‫א‬‫א‬  K‫א‬‫א‬E٧J ١١F  Evaluation of Sine Wave‫א‬‫א‬‫א‬٢J ٣J ١١  ،E٨J ١١F‫א‬‫א‬   ‫א‬‫א‬ K‫א‬ - ٢٣٥ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬  ‫א‬   0 90 180 270 360 ‫א‬‫א‬   ‫א‬‫א‬E٨J ١١F  Representation of Sine Wave‫א‬‫א‬‫א‬٣J ٣J ١١ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ω‫א‬ Em‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ωt‫א‬‫א‬  KE٩J ١١F 1 0.5 ωt 0 ωt π -0.5 -1   K‫א‬‫א‬‫א‬E٩J ١١F - ٢٣٦ - 2π  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Mathematical Representation of Vectors‫א‬‫א‬٤J ٣J ١١  W‫א‬‫א‬  K‫א‬‫א‬‫א‬ K١ K‫א‬‫ א‬K٢ K‫א‬‫ א‬K٣ K‫א‬‫ א‬K٤ ،‫א‬‫א‬‫א‬  WA   A = a 1 + ja 2         E٢J ١١F     − 1 Z‫א‬‫א‬‫א‬‫א‬ Wj ‫א‬‫א‬‫א‬‫א‬  KE١٠J ١١F‫א‬ to - ∞ 0   to ∞   ‫א‬‫א‬‫א‬E١٠J ١١F  j‫א‬‫א‬،X ‫א‬  W   X ⋅ j ⋅ j = −X   KEE–FF‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬، j‫א‬‫א‬ ‫א‬‫א‬K90‫א‬‫א‬‫א‬‫א‬j‫א‬،90 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE١١J ١١F‫א‬‫א‬‫א‬ - ٢٣٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     j  a2  ⎟A⎢    θ  a1  ‫א‬‫א‬‫א‬‫א‬E١١J ١١F   A = (a 12 + a 22 )    ⎞ ⎟⎟  ⎠   ⎛a2 ⎝ a1  θ = tan −1 ⎜⎜     E٣J ١١F    E٤J ١١F   ‫א‬‫א‬‫א‬‫א‬‫א‬EACF‫א‬‫א‬٤J ١١  Alternating Current and Voltage as a Sine Wave.  ‫א‬‫א‬‫א‬١J ٤J ١١  W‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬E١٢J ١١F - ٢٣٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W  K‫א‬‫א‬‫א‬WF ،،‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  + -       ‫א‬‫א‬‫א‬‫א‬E١٣J ١١F  K‫א‬‫א‬‫א‬‫א‬‫א‬   W  K‫א‬‫א‬‫א‬‫ א‬K١  W،‫א‬‫א‬‫א‬‫ א‬K٢   Vs     ‫א‬‫א‬‫א‬‫א‬E١٤J ١١F  - ٢٣٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬٢J ٤J ١١  W‫א‬‫א‬W  WE١٥J ١١F‫א‬‫א‬‫א‬E١٢J ١١F‫א‬   +  R  -  I   ‫א‬‫א‬‫א‬‫א‬E١٥J ١١F  ‫א‬‫א‬‫א‬،‫א‬‫א‬  ‫א‬  EEJ F‫א‬‫א‬EHF‫א‬‫א‬F‫א‬ ‫א‬‫א‬ K‫א‬‫א‬‫א‬K   W‫א‬‫א‬W  +  WE١٦J ١١F  I  R     ‫א‬‫א‬‫א‬‫א‬E١٦J ١١F  ‫א‬‫א‬‫א‬‫א‬W‫א‬،‫א‬  ‫א‬KE‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬، - ٢٤٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬ ‫א‬ K ‫א‬‫א‬ ‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬K ‫א‬‫א‬  K   Sine wave Voltage Sources E‫א‬F‫א‬‫א‬٣J ٤J ١١   W‫א‬‫א‬‫א‬  Rotating Electrical machines‫א‬‫א‬‫א‬K١  AC Generator‫א‬‫א‬     Electronic Oscillator Circuits‫א‬‫א‬‫א‬K٢  Signal Generators‫א‬‫א‬‫א‬   ‫א‬EACF‫א‬‫א‬‫א‬٥J ١١  Alternating Current & Voltage Values of a Sine Wave  ‫א‬‫א‬‫א‬١J ٥J ١١ ‫א‬،‫א‬‫א‬‫א‬  W Instantaneous Value ‫א‬‫ א‬K١ Peak ValueE‫א‬‫א‬F K٢ Root Mean Square (RMS Value)‫א‬‫א‬ K٣  - ٢٤١ - Average Value‫א‬‫ א‬K٤  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Instantaneous Value ‫א‬‫ א‬٢-٥-١١ ،‫א‬E ‫א‬F‫א‬E ‫א‬F‫א‬‫א‬  KE١٧J ١١F‫א‬   ‫א‬‫א‬‫א‬E١٧J ١١F  Peak ValueE‫א‬‫א‬F ٣-٥-١١ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ K ‫א‬  K Peak Value = Amplitude =Magnitude    E١J ١١F W‫א‬‫א‬‫א‬‫א‬ E١J ١١F‫א‬‫א‬E١٨J ١١F - ٢٤٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  V P = 8V  Peak to Peak Value‫א‬‫א‬‫ א‬٤-٥-١١  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W V PP = 2V P  I PP = 2 I P E٥J  ١١F  W‫א‬‫א‬   ‫א‬‫א‬‫א‬E١٩J ١١F  Effective value of sine wave‫اﻟﻘﻴﻤﺔ اﻟﻔﻌﺎﻟﺔ ﻟﻠﻤﻮﺟﺔ اﻟﺠﻴﺒﻴﺔ‬٥J ٥J ١١ ERoot Mean Square (RMS Value ‫א‬‫א‬   ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   R.M.S ‫א‬K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬Root Mean Square‫א‬ ‫א‬،‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬  (VP , I P ) ‫א‬‫א‬ ‫א‬‫א‬‫א‬  W (V PP , I PP ) ‫א‬‫א‬ - ٢٤٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Vrms = 0.707V P  I rms = 0.707.I P   V P = 1.414Vrms  I P = 1.414 I rms  V PP = 2.828Vrms  I PP = 2.828I rms         E٦J ١١F   E٧J ١١F E٨J ١١F  W ‫א‬‫א‬‫א‬،‫א‬‫א‬K١  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Effective value‫א‬‫א‬ ‫א‬K٢  K‫א‬‫א‬‫א‬K‫א‬  Average value of sine wave‫א‬‫א‬‫א‬٦J ٥J ١١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KZ‫א‬‫א‬،(T)‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬T/2‫א‬‫א‬‫א‬ T/2‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬W،E٢٠J ١١F‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬T/2‫א‬‫א‬  KZ‫א‬‫א‬K‫א‬ Im 1 0.75 Iav 0.5 0.25 0 0 30 60 90 120 150 180  ‫א‬‫א‬‫א‬‫א‬E٢٠J ١١F ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬  V avg = 0.637V P = 0.9V rms  I avg = 0.637 I P = 0.9 I rms  - ٢٤٤ -   W،  E٩J ١١F  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬E٢١J ١١F   E٢J ١١F W‫א‬‫א‬ V P , V PP , Vrms , Vavg   E٢J ١١F‫א‬‫א‬E٢٢J ١١F     ‫א‬ V p = 5V VPP = 10V Vrms = 0,707 * VP = 3.535V Vovg = 0,634VP = 3.535V  ‫א‬‫א‬‫א‬‫א‬٦J ١١  Ohm's Law and Kirchhoff's Laws in AC Circuits  ١J ٦J ١١ ‫א‬‫א‬AC ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬،DC‫א‬‫א‬‫א‬ ‫א‬Phase Angle‫א‬‫א‬‫א‬ ‫א‬‫א‬K ‫א‬‫א‬  K - ٢٤٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Ohm's Law in AC Circuits‫א‬‫א‬‫א‬٢J ٦J ١١ ،‫א‬Current‫א‬،  ‫א‬KResistor‫א‬{‫א‬‫א‬Voltage‫א‬،   W‫א‬‫א‬‫א‬  I= V V ⇒ V = I .R ⇒ R = R I E١٠J ١١F    Vs + -  V R   I   E٢٣J ١١F  W  K‫א‬‫א‬‫א‬‫א‬ K١ Same Phase angleE‫א‬F‫א‬‫א‬‫ א‬K٢ ‫א‬‫א‬‫א‬AC‫א‬‫א‬ K٣ RMS ValueAverage ValuePeak Value ‫א‬‫א‬W‫א‬  K  E٣J ١١F  W‫א‬‫א‬‫א‬  Vs Vp=100V  R1= 1kΩ  R2= 560Ω  E٣J ١١F‫א‬‫א‬‫א‬E٢٤J ١١F - ٢٤٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    K‫א‬ E١ K‫א‬‫א‬‫א‬ E٢ RT = R1 + R2 = 1.56kΩ W‫א‬‫א‬‫א‬    ‫א‬ I rms = Vs (rms ) RT ‫א‬‫א‬‫א‬  W،‫א‬‫א‬‫א‬‫א‬‫א‬  V S (rms ) = 0.707V P = 70.7V  W   ⇒ I rms = 45.3mA  W R2 , R1 ‫א‬ V1(rms ) = I rms R1 = 45.32V  V2(rms ) = I rms R2 = 25.38V   ‫א‬‫א‬‫א‬‫א‬٣J ٦J ١١  Kirchhoff's Voltage & Current Laws in AC Circuits ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬،  F‫א‬‫א‬‫?א‬K ‫א‬ ‫א‬‫א‬‫א‬‫א‬?K?‫א‬E ‫א‬‫א‬‫א‬K?‫א‬‫א‬‫א‬،‫א‬‫א‬  W‫א‬‫א‬   W vs = v1 + v2 + v3 + ..........   ∑ I Entering = ∑ I Leaving   E١١J ١١F  W   E١٢J ١١F     K‫א‬‫א‬‫א‬‫א‬‫א‬ - ٢٤٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬١J ٣J ٦J ١١  Kirchhoff's Voltage Law in AC Circuits  W‫א‬‫א‬،‫א‬‫א‬ R1 R2 V1 V2 Rn  Vn    ‫א‬‫א‬E٢٥J ١١F  W‫א‬‫א‬‫א‬   Vs ( rms ) = V1( rms ) + V2( rms ) + ..... + VN ( rms )        E١٣J ١١F   Vs ( P ) = V1( P ) + V2( P ) + ..... + VN ( P )        E١٤J ١١F    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬٢J ٣J ٦J ١١  Kirchhoff's Current Law in AC Circuits  W‫א‬‫א‬،‫א‬‫א‬ A  I I1 R1 I2 In  R1 R2   B   ‫א‬‫א‬‫א‬E٢٦J ١١F   W‫א‬‫א‬‫א‬ I ( rms ) = I 1( rms ) + I 2( rms ) + .... + I N ( rms )     I ( PP ) = I 1( PP ) + I 2 ( PP ) + .... + I N ( PP )           E١٦J ١١F - ٢٤٨ -  E١٥J ١١F    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   E٤J ١١F  ‫ ؟‬R3 ‫א‬Peak Value‫א‬‫א‬  KR.M.S Value‫א‬ ‫א‬‫א‬‫א‬‫א‬W  R1   12V VS 24V  R2 8V R3  V3    E٤J ١١F‫א‬‫א‬‫א‬E٢٧J ١١F  ‫א‬  W V3 ‫א‬   RMS‫א‬ V S ( rms ) VS = V1 + V2 + V3 = V 1 ( rms + V 2 ( rms ) + V 3 ( rms )    V3 ‫א‬‫א‬‫א‬   ) V3( rms ) = 4V  W V3 ‫א‬‫א‬∴ V3( P ) = 1.414V3( rms ) = 5.66V - ٢٤٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٥J ١١F  W ‫א‬‫א‬‫א‬ Itotal Vs   10A  R3  3A    E٥J ١١F‫א‬‫א‬‫א‬E٢٨J ١١F  I avg ‫א‬‫א‬،RMS‫א‬‫א‬   ‫א‬  W I tot ( rms ) ‫א‬  I Τ( rms ) = I 1( rms ) + I 2 ( rms ) = 10 + 3 = 13 A  E I Τ( P ) F‫א‬‫א‬‫א‬∴   I Τ( P ) = 1.414 × I t ( rms ) = 18.382 A   I t ( avg ) EF‫א‬‫א‬‫א‬ I Τ( avg ) = 0.637 * I Τ( P ) = 11.7 A  - ٢٥٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E‫א‬F٧J ١١  Superimposed DC and AC voltage  ١J ٧J ١١ ‫א‬،‫א‬   W‫א‬K‫א‬‫א‬،‫א‬،   Vs  V=Vs+Vdc   VDC   E٢٩J ١١F  ‫א‬‫א‬‫א‬‫א‬‫א‬  E‫א‬‫א‬‫א‬‫א‬F‫א‬،‫א‬‫א‬  W‫א‬‫א‬،‫א‬   VDC > VP ‫א‬‫א‬‫א‬‫א‬  ٢-٧-١١  W‫א‬‫א‬،‫א‬  V DC  > VP E٣٠J ١١F   K VDC + V p W‫א‬‫א‬‫א‬،  K VDC − VP W‫א‬‫א‬ - ٢٥١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬،‫א‬   V DC < V P ‫א‬‫א‬‫א‬‫א‬  ٣-٧-١١  W‫א‬‫א‬،‫א‬   V DC < V P E٣١J ١١F   K VDC + V p W‫א‬‫א‬‫א‬،  K VDC − VP W‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬   E٦J ١١F  W‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  Vp= 10V R=1k VDc= 12V     E٦J ١١F‫א‬‫א‬‫א‬E٣٢J ١١F - ٢٥٢ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬  W R ‫א‬‫א‬‫א‬  Vmax = VDC + VP = 12V + 10V = 22V  W R ‫א‬‫א‬‫א‬  Vmin = VDC − V p = 12V − 10V = 2V  ‫א‬‫א‬‫א‬ ‫א‬  K‫א‬‫א‬   ‫א‬‫א‬‫א‬E٣٣J ١١F   E٧J ١١F  R‫א‬‫א‬‫א‬   Vp= 10V  R  VDC= 6V   E٧J ١١F‫א‬‫א‬‫א‬E٣٤J ١١F   ‫א‬  ‫א‬‫א‬  Vmax = VDC + V p = 16v  ‫א‬‫א‬  Vmin = VDC − VP = −4V  W‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ - ٢٥٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬‫א‬E٣٥J >>F   Non Sinusoidal Wave Forms‫א‬‫א‬٨J ١١  ١J ٨J ١١ ‫א‬K  ‫א‬،‫א‬‫א‬  ‫א‬‫א‬،‫א‬‫א‬‫א‬  ‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ Repetitive Pulse Wave Form E‫א‬F K١ Square Wave ‫א‬‫ א‬K٢ Triangular Wave Form‫א‬‫ א‬K٣  Saw tooth Wave Form‫א‬ K٤ Harmonics‫א‬‫ א‬K٥  K‫א‬،  Repetitive Pulse Wave Form E‫א‬F ٢-٨-١١   W‫א‬‫א‬‫א‬‫א‬    Tw T   ‫א‬E٣٦J ١١F - ٢٥٤ -    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ، T ‫א‬‫א‬ ‫א‬K Period ‫א‬‫א‬  (Baseline )  W‫א‬  Amplitude Baseline  ‫א‬  ‫א‬‫א‬E٣٧J ١١F   K‫א‬    ،E F‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K  ‫א‬‫א‬ KPractical Pulse Wave Form‫א‬   ‫א‬‫א‬E٣٨J ١١F  W،‫א‬ ‫א‬ 90% 10% ‫א‬‫א‬‫א‬WRise Time (Tr ) ‫א‬ K١ KAmplitude‫א‬ - ٢٥٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬10%  90% ‫א‬‫א‬‫א‬WFall Time (TF ) ‫א‬ K٢ K‫א‬  50% ‫א‬N, M ‫א‬‫א‬WPulse Width  (TW ) ‫א‬ K٣ KA‫א‬‫א‬  W‫א‬  The duty Cycle‫א‬ K٤   Tw T    ‫א‬‫א‬E٣٩J ١١F ‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬  W‫א‬‫א‬  ⎛T ⎞ P.D.C = ⎜ w ⎟ *100%  ⎝T ⎠        E١٧J ١١F  KPercent Duly Cycle‫א‬‫א‬E P.D.C F Average Value‫א‬‫ א‬K٥    Amplitude V baseline     T  Vavg = Vbaseline +  Tw = Amplitude T  ‫א‬‫א‬E٤٠J ١١F - ٢٥٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   Vovg = Vbaseline +  Tw * Amplitude T E٨J ١١F   E٨J ١١F  W‫א‬‫א‬   E٨J ١١F‫א‬‫א‬E٤١J ١١F  K‫א‬‫א‬، P.D.C ‫א‬‫א‬،F‫א‬،T‫א‬    ‫א‬ 1 1 = = 100kH Z  T 10µs 1 ⎛T ⎞ Percent duty Cycle= ⎜ W ⎟100% = * 100% = 10% 10 ⎝ T ⎠ Q T = 10µs ⇒ F =    K‫א‬ 10% ‫א‬  V avg = Vbaseline + = 1V + TW * amplitude T 1µs * (5V − 1V ) = 1.4V 10 µs  Square Wave‫א‬‫ א‬٣-٨-١١  ‫א‬‫א‬‫א‬‫א‬‫א‬  W،T‫א‬Z‫א‬ ⇐ 50%  TW = T 2           E١٩J ١١F  W‫א‬‫א‬‫א‬ - ٢٥٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬E٤٢J ١١F  TW =  W T 2  Triangular Wave Form‫א‬‫ א‬٤-٨-١١  W‫א‬ T      EJ ٤٣J ١١F     V avg  EJ ٤٣J ١١F  ‫א‬ ‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬  W‫א‬،‫א‬   V t Slope = V\t  t Slope =- V\t  ‫א‬‫א‬E٤٤J ١١F - ٢٥٨ -    ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٩J ١١F  WE‫א‬‫א‬F‫א‬ V V 10 v 10 v     2v 5 sec 3 sec t  t  E٩J ١١F‫א‬‫א‬E٤٥J ١١F  ‫א‬ v 10v = = 2V / s t 5s v 10v − 4v slope = − = − t 3ms 6 = − V / ms 3 = −2kV / s slope =  Saw tooth Wave Form‫א‬ ٥-٨-١١ ،‫א‬‫א‬‫א‬  W‫א‬،‫א‬  V T  t  ‫א‬E٤٦J ١١F - ٢٥٩ -     ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ،‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬K  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  K‫א‬ Harmonics‫א‬‫ א‬٦-٨-١١  K ‫א‬‫א‬  W‫א‬  K Fo ‫א‬‫א‬‫א‬W K١ ‫א‬،W‫א‬ K٢  2 F0 ,3Fo ,4 Fo ,5Fo .....        W‫א‬    E٢٠J ١١F  W‫א‬‫א‬ Odd Harmonics‫א‬ K  W،‫א‬‫א‬‫א‬‫א‬  3F0 ,5 Fo ,7 Fo ,9 Fo .....            E٢١J ١١F  Even Harmonics‫א‬ K  W،‫א‬‫א‬‫א‬‫א‬ 2 Fo 4 Fo 6 Fo 8Fo .....          E٢٢J ١١F   ،‫א‬‫א‬‫א‬ ‫א‬K  KEF‫א‬،‫א‬   W‫א‬،‫א‬‫א‬‫א‬ - ٢٦٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬          To Fo =1/To  ‫א‬‫א‬E٤٧J ١١F   Fo ‫א‬‫א‬   T1 = T 1 = o 3Fo 3 3Fo ١‫א‬‫א‬   K‫א‬‫א‬‫א‬٣، To ‫א‬   To ⇐ 5 Fo ٢‫א‬‫א‬ 5 T T3 = o ⇐ 7 Fo ٣‫א‬‫א‬ 7 T2 =    ١‫א‬‫א‬‫א‬‫א‬E٤٨J ١١F    ٣،٢،١‫א‬‫א‬‫א‬‫א‬E٤٩J ١١F - ٢٦١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Summary‫א‬ K‫א‬‫א‬‫א‬‫ א‬K١ ‫א‬‫א‬‫א‬‫א‬‫א‬ K٢ Kω‫א‬Em‫א‬ WE‫א‬F‫א‬‫א‬ K٣ ‫א‬‫א‬‫• א‬ ‫א‬‫א‬‫א‬ • W،‫א‬‫א‬‫א‬ K٤ Instantaneous Value ‫א‬‫• א‬ Peak ValueE‫א‬‫א‬F • Root Mean Square (RMS Value)‫א‬‫א‬ •   Average Value‫א‬‫• א‬ vs = v1 + v2 + v3 + .......... W ∑I Entering = ∑ I Leaving K٥ W K٦  K‫א‬‫א‬‫א‬‫א‬‫א‬ K٧ ‫א‬‫א‬‫א‬‫א‬‫א‬ K٨ E‫א‬‫א‬‫א‬‫א‬F‫א‬،‫א‬‫א‬ K‫א‬ W،‫א‬ K٩ Repetitive pulse wave form E‫א‬F • Square Wave ‫א‬‫• א‬ Triangular Wave Form‫א‬‫• א‬  Saw tooth Wave Form‫א‬ • Harmonics‫א‬‫• א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬K١٠ - ٢٦٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬  W‫א‬W  ‫א‬‫א‬‫א‬‫א‬‫ א‬K ‫א‬‫א‬‫ א‬K  ‫א‬‫א‬ K  K ‫א‬‫א‬‫א‬‫ א‬K   W‫א‬W  12V ‫א‬‫א‬ .١   V AVG ‫א‬‫א‬ V PP ‫א‬‫א‬‫א‬ RMS ‫א‬  ‫א‬‫א‬‫א‬ R1 R2 ‫א‬‫א‬K٢ RMS  R1=470   R3= 1kΩ Vs R2  Vf=110V R4 V4=65V  V4=30V     VS 24V  RMS  R3 ‫א‬‫א‬K٣  R1 12V 8V R3 V3 - ٢٦٣ - R2  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬‫א‬K٤   ‫؟‬‫א‬‫؟‬‫א‬   - ٢٦٤ -  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬ ١٢  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬     W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬  W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   - ٢٦٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬    Introduction١J ١٢ ‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،Transformers‫א‬‫א‬  W Mutual InductanceE‫א‬F‫א‬‫ א‬K١ The Basic Transformer ‫א‬‫ א‬K٢ Step up – Transformer‫א‬ K٣  Step –down Transformer ‫א‬ K٤   Mutual Inductance ‫א‬‫א‬٢J ١٢ ، ‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬ ،Inductor ‫א‬ ‫א‬‫א‬K   ‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬  ‫ﻣﺠﺎل‬ ‫ﻣﻐﻨﺎﻃﻴﺴﻲ‬   ‫ﺑﻄﺎرﻳﺔ‬  ‫א‬‫א‬EJ ١J ١٢F      K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  - ٢٦٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬    The Basic Transformer‫א‬‫א‬٣J ١٢   Structure١J ٣J ١٢ K‫א‬‫א‬  W‫א‬  Source Primary winding Secondary winding  Load   ‫א‬‫א‬EJ ١J ١٢F   W  ‫א‬‫א‬ ‫א‬Primary Winding‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬Secondary Winding ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬   ‫א‬‫א‬‫א‬The Core ‫א‬‫א‬  K‫א‬‫א‬   - ٢٦٧ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬٢J ٣J ١٢  W،‫א‬‫א‬  W‫א‬‫א‬Air Core ‫א‬ K١       ‫א‬‫א‬‫א‬‫א‬E٢J ١٤F W‫א‬Ferrite Core K٢       ‫א‬E٣J ١٢F W‫א‬Iron Core  K٣       ‫א‬‫א‬E٤J ١٢F - ٢٦٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬    ،High Frequency Applications ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Power Applications ‫א‬‫א‬‫א‬‫א‬Iron Core ‫א‬‫א‬  KAudio Frequency Applications‫א‬‫א‬‫א‬‫א‬‫א‬   ٣J ٣J ١٢  W‫א‬،‫א‬‫א‬  W‫א‬،Core –type ‫א‬‫א‬،W  ‫א‬E٥J ١٢F W‫א‬،Shell – type ‫א‬‫א‬‫א‬‫א‬W ‫א‬E٦J ١٢F   KVarnish ‫א‬‫א‬،‫א‬   Turns Ratio‫א‬‫א‬٤J ١٢  ‫א‬ N sec ‫א‬‫א‬‫אא‬E N F‫א‬  W‫א‬‫א‬، N pri ‫א‬‫א‬  N= N Sec N Pr i            E١J ١٢F  - ٢٦٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬     E١J ١٢F  W‫א‬‫א‬     100: 400 ‫ﻟﻔﺔ‬ ‫ﻟﻔﺔ‬  E١J ١٠F‫א‬‫א‬‫א‬E٧J ١٢F      N Pr i = 100  N sec = 400  N=  W N Sec 400 = =4 N Pr i 100  W‫א‬‫א‬ ١:٤        ‫א‬E٨J ١٢F   K‫א‬‫א‬٤‫א‬‫א‬‫א‬‫א‬ - ٢٧٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬    Direction of Winding‫א‬‫א‬٤J ١٢ ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬،E‫א‬‫א‬F‫א‬  W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬  ‫א‬،‫א‬  W‫א‬KPrimary and Secondary are in phase ‫א‬     ‫א‬‫א‬‫א‬E٩J ١٢F  W‫א‬‫א‬  + -  +   -  ‫א‬‫א‬‫א‬‫א‬‫א‬E١٠J ١٢F      K‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬،‫א‬  W‫א‬‫א‬‫א‬ - ٢٧١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬        ‫א‬‫א‬E١١J ١٢F     W‫א‬، T = 180 0 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ١٢F  W‫א‬‫א‬  +  -  +  ‫א‬‫א‬‫א‬‫א‬E١٣J ١٢F  - ٢٧٢ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬    Inductance Voltage and Current Relationship ‫א‬‫א‬‫א‬٥J ١٢  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٥J ١٢  Primary and Secondary Voltage Relationship ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ E  ‫א‬‫א‬‫א‬F‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  WE‫א‬‫א‬F‫א‬‫א‬  V SEC N SEC = =N V PRI N PRI         E٢J ١٢F  W  ⎛N ⇒ V SEC = ⎜⎜ SEC ⎝ N PRI ⎞ ⎟⎟V PRI = N * V PRI  ⎠        E٣J ١٢F  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥J ١٢  Primary and Secondary Current Relationship E‫א‬‫א‬F‫א‬ ،E  ‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬ Ipri  Isec   Vpri  Vsec   Npri  Nsec  ‫א‬‫א‬‫א‬‫א‬‫א‬E١٤J ١٢F   W I sec ‫א‬‫א‬ I PRI ‫א‬‫א‬‫א‬‫א‬‫א‬  I sec N 1 = PRI = I PRI N sec N     - ٢٧٣ -      E٤J ١٢F  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬     W  ⎛N ⇒ I sec = ⎜⎜ PRI ⎝ N sec ⎞ I ⎟⎟ * I PRI = PRI N ⎠         E٥J ١٢F   ‫א‬‫א‬‫א‬‫א‬ ‫א‬  W  K‫א‬‫א‬ step − up  K١  K‫א‬‫א‬ step − down  K٢  Transformer Types ‫א‬‫א‬٦J ١٢  Step–up Transformer١J ٦J ١٢ E  ‫א‬‫א‬F‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ K١‫א‬KE  ‫א‬‫א‬‫א‬F‫א‬‫א‬ ‫א‬ N SEC > N PRI    V SEC > V PRI      W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬       N > 1        E٦J ١٢F      E٧J ١٢F ،١‫א‬    W V SEC > V PRI ‫א‬‫א‬‫א‬‫א‬‫א‬   I SEC < I PRI ‫א‬‫א‬‫א‬‫א‬‫א‬  Step–down Transformer٢J ٦J ١٢   E  ‫א‬‫א‬F‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬K١‫א‬KE  ‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬  N SEC < N PRI     W‫א‬‫א‬‫א‬K‫א‬‫א‬         E٨J ١٢F N < 1 ،١‫א‬ - ٢٧٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬      I SEC  V SEC < V PRI ‫א‬‫א‬‫א‬‫א‬‫א‬ > I PRI ‫א‬‫א‬‫א‬‫א‬‫א‬،  E٢J ١٢F ‫א‬،٦٠٠‫א‬‫א‬،٢٠٠‫א‬‫א‬  ‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬ Ipri = 6A Isec    Vsec Vpri 12Drms  R    E٢J ١٢F‫א‬‫א‬‫א‬E١٥J ١٢F   ‫א‬  ⎛N V SEC (rms ) = ⎜⎜ SEC ⎝ N PRI   ⎞ 600 ⎟⎟ * V PRI (rms ) = * 120 = 360V 200 ⎠ = N *V PRI (rms ) = 3 *120 = 360V ⎛N I SEC (rms ) = ⎜⎜ PRI ⎝ N SEC  ⎞ 200 ⎟⎟ * I PRI (rms ) = * 6 = 2A 600 ⎠  K‫א‬‫א‬‫א‬   ‫א‬KStep– up Transformer‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  - ٢٧٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬     E٣J ١٢F  W‫א‬‫א‬‫א‬‫א‬‫א‬ Ipri= 6A  Isec   Vsec Vpri  R  120rms  50 : 10  E٣J ١٢F‫א‬‫א‬‫א‬E١٦J ١٢F  ‫א‬ N SEC 10 * 120 = 24V * V PRI ( rms ) = N PRI 50 N 50 * 6 A = 30 A = PRI * I PRI (rms ) = N SEC 10  V SEC (rms ) =  I SEC (rms ) ‫א‬  ‫א‬KStep– down Transformer ⇐ ‫א‬‫א‬‫א‬  K    Transformer Current Direction ‫א‬‫א‬‫א‬٧J ١٢  W،‫א‬‫א‬  W‫א‬،E‫א‬‫א‬F‫א‬‫ א‬K١   + _ + _ + _ R    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EJ ١٧J ١٢F - ٢٧٦ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬      + _ + _ + _ R   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EJ ١٧J ١٢F W‫א‬،E‫א‬F‫א‬‫ א‬K٢    + _ + _ + _ R     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EJ ١٨J ١٢F   + _  + _   + _ R ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EJ ١٨J ١٢F - ٢٧٧ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬     Summary‫א‬ K‫א‬‫א‬‫א‬‫א‬ K١ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٢  K‫א‬‫א‬‫א‬ K‫א‬Primary Winding‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬ K٣  K‫א‬‫א‬Secondary Winding ‫א‬‫א‬W‫א‬‫ א‬K٤ ‫א‬‫א‬ ‫א‬ N sec ‫א‬‫א‬‫אא‬E N F‫א‬ K٥ K N pri ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫ א‬K٦  WE‫א‬‫א‬F‫א‬‫א‬E‫א‬‫א‬  V SEC N SEC = =N V PRI N PRI  W I sec ‫א‬‫א‬ I PRI ‫א‬‫א‬‫א‬‫א‬‫א‬ K٧  I sec N 1 = PRI = I PRI N sec N  ‫א‬‫א‬‫א‬‫א‬ ‫א‬ K٨ W  K‫א‬‫א‬ step − up  K   K‫א‬‫א‬ step − down  K - ٢٧٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬ W‫א‬‫א‬‫א‬‫א‬،‫א‬ K١    Irms = 20A W‫א‬ K٢  1 : 10  Vpri 10Vrms  R      Vsec(avg ) ‫א‬‫א‬‫א‬ K١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،E‫א‬F‫א‬‫א‬ K٢  ‫؟‬‫א‬‫א‬ - ٢٧٩ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬  ‫א‬  ‫א‬    W‫א‬ K٣ 2 : 1    R 30Vrms  I =100mArms  ‫؟‬‫א‬‫א‬‫א‬ K١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫؟‬‫א‬‫א‬‫א‬ K‫א‬‫א‬ - ٢٨٠ - .٢   ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ١٣  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٤ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬  W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   - ٢٨١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction١J ١٣ ، ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬K ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬، AC ‫א‬‫א‬‫א‬K µs  ‫א‬Frequency‫א‬‫א‬‫א‬،  KCapacitance   Capacitive Reactance X C ‫א‬‫א‬٢J ١٣  W‫א‬‫א‬، X C ‫א‬‫א‬  ‫א‬‫א‬ ‫א‬، ‫א‬‫א‬  W‫א‬،‫א‬‫א‬‫א‬‫א‬ F  V   I  C     ‫א‬‫א‬‫א‬‫א‬EJ ١J ١٣F   ‫א؟‬K‫א‬‫א‬،F‫א‬‫א‬   ‫א‬EJ ١J ١٣F - ٢٨٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬E٢F‫א‬،‫א‬E١F‫א‬،EJ ١J ١٣F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬t ،  K V2 > V1  K I 2 > I 1 ،‫א‬ ⇐ ‫א‬ ⇐ Q = CV ⇐C = Q  V ‫א‬‫א‬ ⇐ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬،‫א‬‫א‬EF‫א‬‫א‬‫א‬    ،Capacitive Reactance X C ‫א‬‫א‬‫א‬‫א‬  K Ohm(Ω) W X C ‫א‬‫א‬   ‫א‬‫א‬ ‫א‬‫א‬‫א‬  W‫א‬،‫א‬‫א‬ Fo  V   I   C     ‫א‬‫א‬‫א‬‫א‬EJ ١J ١٣F  K   ‫א‬‫א‬ ⇐ ‫א‬،‫א‬،  W،Capacitive Reactance Formula‫א‬‫א‬‫א‬  XC = 1  2π .F .C      - ٢٨٣ -      E١J ١٣F  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E١J ١٣F  W‫א‬‫א‬‫א‬   C=0.005µF    E١J ١٣F‫א‬‫א‬‫א‬E٢J ١٣F   K F = 1kHz ‫א‬‫א‬، X C ‫א‬‫א‬   XC =  ‫א‬ 1 1 = = 31.8kΩ 3 2πF .C 2π * 1 * 10 * 0.005 * 10 − 6   ‫א‬‫א‬‫א‬‫א‬٣J ١٣  Ohm's Law in Capacitive AC Circuits ،‫א‬‫א‬ ،E٣J ٣F‫א‬  WK‫א‬‫א‬،‫א‬  Q ∝ V  Q = CV            E٢J ١٣F          E٣J ١٣F ‫א‬‫א‬،‫א‬C‫א‬‫א‬‫א‬  K Farad‫א‬‫א‬ - ٢٨٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     i   ++++ Q E  ----    K‫א‬‫א‬‫א‬‫א‬E٣J ١٣F  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬،  V = I * XC       V XC V XC = I             I=  W،      E٤J ١٣F       E٥J ١٣F       E٦J ١٣F  W‫א‬‫א‬‫א‬‫א‬   V I   R   ‫א‬E٤J ١٣F     Peak  RMS ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K Peak − to − Peak - ٢٨٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٢J ١٣F  W،5V‫א‬‫א‬،E١J ١٣F‫א‬‫א‬‫א‬  C=0.005µF Vs 1kHz     E٢J ١٣F‫א‬‫א‬‫א‬E٥J ١٣F   K I P  Peak ‫א‬   ‫א‬  W، I P ‫א‬ W‫א‬‫א‬ X C ، I P  K١  XC = 1 1 = − = 3.18kΩ 3 2πFC 2π 10 * 10 * 0.005 * 10 −6 ( ) ( ) W I r .m.s  K٢ I rms = V rms 5 = = 1.57 mA X C 3.18 * 10 3  W I P  I r .m.s ‫א‬ K٣  I P = 1.414 * I rms = 2.22mA   ‫א‬‫א‬‫א‬‫א‬٤J ١٣ Current & Voltage Relationship in Capacitive Circuits ‫א‬‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬،KEE VR and I R )are in Phase)،‫א‬ ‫א‬‫א‬‫א‬‫א‬، 90 o ‫א‬Leads  KEPhase Shift) - ٢٨٦ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬‫א‬‫א‬E٦J ١٣F  Power in Capacitor Circuits ‫א‬‫א‬‫א‬٥J ١٣ ‫א‬DC‫א‬ ‫א‬‫א‬‫א‬، ،‫א‬‫א‬‫א‬‫א‬K ‫א‬، P = V .I ‫א‬ ،‫א‬‫א‬‫א‬K  W‫א‬‫א‬‫א‬   Instantaneous Power‫א‬‫א‬١J ٥J ١٣ E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬E٧J ١٣F    K‫א‬‫א‬‫א‬‫ א‬K١ K‫א‬‫ א‬K٢ ‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬K  ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،  ‫א‬ ‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ - ٢٨٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬  K  True Power Ptrve ‫א‬‫ א‬٢J ٥J ١٣ ‫א‬‫א‬، ‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬  Ptrue = 0          W‫א‬‫א‬‫א‬     E٧J ١٣F ،‫א‬Leakage‫א‬‫א‬،‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬  K‫א‬‫א‬ Pr Reactive Power‫א‬‫א‬٣J  ،‫א‬ ‫א‬‫א‬‫א‬  Pr = Vrms * I rms   Pr =  V rms 2  XC         2 Pr = I rms * C   ٥J ١٣  W‫א‬‫א‬‫א‬      E٨J ١٣F       E٩J ١٣F       E١٠J ١٣F   W  Kwatt‫א‬‫א‬ Ptrue ‫א‬‫א‬K١  VAR‫א‬‫א‬Volt – Ampere –Reactive Pr ‫א‬‫א‬K٢  - ٢٨٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٣J ١٣F  W‫א‬‫א‬‫א‬  Vrms= 2V C=0.01µF F2=2kHz    E٣J ١٣F‫א‬‫א‬‫א‬E٨J ١٣F   ‫؟‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  Ptrue = 0W  Pr =  1 = 7.96kΩ 2π .FC 22 ⇒ Pr = = 503 * 10 −6 VAR = 503µVAR 7.96 * 10 3  Vrms XC 2 XC =  Series & Parallel Capacitive AC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٦J ١٣ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬ W،‫א‬ Series Capacitors ‫א‬‫א‬‫א‬١J ٦J ١٣  W‫א‬‫א‬‫א‬‫א‬‫א‬ V1   V2 VN  ‫א‬‫א‬‫א‬E٩J ١٣F - ٢٨٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     CT =   W‫א‬‫א‬‫א‬ 1 1 1 1 + + .... C1 C 2 CN          E١١J ١٣F  W، E١٢J ١٣F X CT = X C! + X C2 + X C N   Parallel Capacitors‫א‬‫א‬‫א‬٢J ٦J ١٣  W‫א‬‫א‬‫א‬‫א‬‫א‬  C1  C2   CN    B A  ‫א‬‫א‬‫א‬E١٠J ١٣F    W‫א‬‫א‬‫א‬ C T = C1 + C 2 + L + C N         1        X CT = 1 1 1 + + .... X C! X C 2 X CN   E١٣J ١٣F  W،  E١٤J ١٣F  - ٢٩٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Series RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١٣  Characteristics of RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٧J ١٣  W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ I R VR Vs F C   VC      ‫א‬‫א‬‫א‬‫א‬‫א‬E١١J ١٣F   ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ I C  ‫א‬‫א‬، ‫א‬ VR ‫א‬ I R  ‫א‬‫א‬‫א‬، ‫א‬K VC  K‫א‬‫א‬‫א‬‫א‬   ، 90 o ‫א‬‫א‬ VC  I C ،‫א‬  ‫א‬K 90 o ‫א‬‫א‬ VC ‫א‬ VR ‫א‬‫א‬  W‫א‬ 90 o ‫א‬‫א‬،‫א‬‫א‬  K VC   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ١٣F + V R ‫א‬‫א‬ VC  V R      K VC  VR ‫א‬‫א‬‫א‬  I ‫א‬  ، θ  VS  VR E١٢J ١٣F‫א‬  ‫א‬K‫א‬‫א‬‫א‬ VR  I  θ  VS  - ٢٩١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ،Phase angle‫א‬‫א‬ θ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K θ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬RC‫א‬  Impedance Z‫ א‬٢J ٧J ١٣ ‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬ F‫א‬، RT ‫א‬E‫א‬F‫א‬‫א‬ ‫א‬‫א‬‫א‬  ، CT ‫א‬‫א‬‫א‬‫א‬  KOhmZ  W‫א‬Series R – C ‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬E١٣J ١٣F  Z 2 = R2 + X C   Z = R2 + X C 2 2         WPythagoras‫א‬‫א‬         E١٥J ١٣F       E١٦J ١٣F  W‫א‬‫א‬RC‫א‬   θ Phase Angle‫א‬‫א‬٣J ٧J ١٣ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ θ   W   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٤J ١٣F - ٢٩٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬ θ ‫א‬‫א‬‫א‬E tan θ F θ ‫א‬‫א‬  W،‫א‬  tan θ = ⎛V VC ⇒ θ = tan −1 ⎜⎜ C VR ⎝ VR ⎞ ⎟⎟ ⎠ EJ ١٧J ١٣F    tan θ = XC ⎛X ⎞ ⇒ θ = tan −1 ⎜ C ⎟ R ⎝ R ⎠ EJ ١٧J ١٣F   (tan ) ‫א‬‫א‬‫א‬‫א‬‫א‬ (tan −1 ) ‫א‬‫א‬W ⎛ VC ⎝ VR  K VC ‫א‬‫א‬‫א‬ θ = tan −1 ⎜⎜ VR ⎞ ⎟⎟ ‫א‬ ⎠   Voltages Relationships‫א‬‫א‬RC‫א‬‫א‬‫א‬٤J ٧J ١٣  VC ‫א‬‫א‬ VR ‫א‬‫א‬ VS ‫א‬  W‫א‬‫א‬   ‫א‬‫א‬Rc‫א‬‫א‬‫א‬E١٥J ١٣F    K‫א‬‫א‬   W‫א‬‫א‬‫א‬،‫א‬‫א‬   ‫א‬‫א‬‫א‬E١٦J ١٣F  2 2 V S = V R + VC 2       WPythagoras‫א‬  - ٢٩٣ -      E١٨J ١٣F  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬  VS = VR + VC  VS = VS − VC  VC = V S − V R 2 2           E١٩J ١٣F 2 2           E٢٠J ١٣F 2 2           E٢١J ١٣F  Ohm's Law‫א‬‫א‬‫א‬‫א‬٥J ٧J ١٣ ،،‫א‬‫א‬  W‫א‬ I  C R    ‫א‬‫א‬RC‫א‬E١٧J ١٣F  W‫א‬‫א‬ VR ‫א‬‫א‬‫א‬‫א‬ V R = I .R             E٢٢J ١٣F  ‫א‬‫א‬ ، X C ‫א‬‫א‬، VC  VC = I . X C        W VC ‫א‬‫א‬‫א‬‫א‬       E٢٣J ١٣F ،E‫א‬‫א‬F V ‫א‬‫א‬‫א‬‫א‬‫א‬  V = I .Z   V Z V Z= I I=         W‫א‬‫א‬‫א‬ RC ‫א‬Z‫א‬             - ٢٩٤ -     E٢٤J ١٣F      E٢٥J ١٣F      E٢٦J ١٣F  W‫א‬‫א‬‫א‬  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬‫א‬،   ‫א‬‫א‬‫א‬E١٨J ١٣F   Frequency Effect on RC ‫א‬‫א‬‫א‬‫א‬٦J ٧J ١٣ K ‫א‬،‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬ K ⎛⎜ X C ⎝ = 1 ⎞ ⎟ ، X C ‫א‬‫א‬‫א‬ F ‫א‬‫א‬ 2πFC ⎠ K١  W ⎛⎜ Z = R 2 + X 2 ⎞⎟ W‫א‬ ⇐ C ⎠ ⎝ KE‫א‬‫א‬F I = V WEF‫⇐ א‬ Z     KVL  VR ‫א‬ ⇐   K (VS 2 = VR 2 + VC 2 ) VC ‫א‬ ⇐  ↑ VC ↓ VR ⇐↓ I  ↑ Z ⇐↑ X C ⇐ F ‫ א‬K٢  W‫א‬‫א‬‫א‬، R = 2.2kΩ, C = 0.02µF , I rms = 0.2mA, f I Vs F R VR   E٤J ١٣F = 1.5kHz ‫א‬ C    VC    E٤J ١٣F‫א‬‫א‬‫א‬E١٩J ١٣F - ٢٩٥ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    XC =  X C ‫א‬‫א‬ 1 1 = = 5.3kΩ −3 2nf .c 2n * 1.5 * 10 * 0.02 * 10 −3 K   Z ‫א‬ K 2 Z = R 2 + X C = 5.73kΩ V R ‫א‬ K  VC ‫א‬ K  V S ‫א‬ K θ ‫א‬‫א‬ K V R = I .R = 0.2 * 10 −3 * 2.2 * 10 3 = 0.44V VCrms = I rrms X C = 0.2 * 10 −3 * 5.3 * 10 −3 = 1.06V (a )  VS rms = V R2( rms ) + VC2( rms ) = 0.44 2 + 1.06 2 = 1.15V (b )  VS rms = I rms * Z = 0.2 * 10 −3 * 5.73 * 10 3 = 1.15V  ⎛ VC ⎝ VR ⎞ ⎟⎟ = 67.45 o ⎠ X (b )  θ = tan −1 ⎛⎜ C ⎞⎟ = 67.45 o ⎝ R ⎠  (a )  θ = tan −1 ⎜⎜  Parallel RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١٣  Characteristics of RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ١٣  W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  VS C F R  ‫א‬‫א‬‫א‬‫א‬‫א‬E٢٠J ١٣F - ٢٩٦ -      ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W VC = VR = VS  • ‫א‬ VR  I R • K 90 o ‫א‬ I P  I C ⇐ ، 90 o ‫א‬‫א‬ VC  I C • ‫א‬‫א‬ RC ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬  K‫א‬‫א‬‫א‬‫א‬ RC ‫א‬‫א‬   ‫א‬‫א‬RC‫א‬‫א‬‫א‬‫א‬‫א‬E٢١J ١٣F   I R  K 90 o ‫א‬‫א‬ I R  I C ‫א‬ ‫א‬ VR  I R ، θ ‫א‬‫א‬ I T  VR   ، θ   I T ‫א‬‫א‬ I T ‫א‬‫א‬E‫א‬‫א‬F  K θ Phase Angle  Impedance Z‫ א‬٢-٨-١٣ ‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬، ،‫א‬‫א‬KOhmZ‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬RC‫א‬‫א‬E٢٢J ١٣F  - ٢٩٧ - IC = VC XC W  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ،Parallel R – C ‫א‬‫א‬‫א‬‫א‬  WAdmittance triangle‫א‬‫א‬   ‫א‬‫א‬RC‫א‬‫א‬E٢٣J ١٣F ، 1 ، Z 1 XC   ، 1 ‫א‬،‫א‬،‫א‬admittance‫א‬ R  K‫א‬‫א‬   W‫א‬‫א‬‫א‬  1 1 1 = 2 + 2 2 Z R XC  X C + R2 1 = Z 2 R2 * X C2 2           E٢٧J ١٣F           E٢٨J ١٣F  W  Z = 2 R2 * XC 2 R + XC 2 2 ⇒Z = R*C R2 + X C 2         E٢٩J ١٣F  Phase Angle θ ‫א‬‫א‬٣J ٨J ١٣ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ θ   W‫א‬‫א‬   ‫א‬‫א‬RC‫א‬‫א‬‫א‬E٢٤J ١٣F - ٢٩٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ،‫א‬‫א‬ θ ‫א‬‫א‬‫א‬E tan θ F θ ‫א‬‫א‬  W  tan θ = IC IR E٣٠J ١٣F  (tan ) ‫א‬‫א‬‫א‬‫א‬‫א‬ (tan −1 ) ‫א‬‫א‬W  K IC IR ⎛ IC ⎝ IR ‫א‬‫א‬‫א‬ θ = tan −1 ⎜⎜ ⎞ ⎟⎟ ‫א‬ ⎠   Currents Relationships‫א‬‫א‬RC‫א‬‫א‬‫א‬‫א‬٤J ٨J ١٣  I C ‫א‬‫א‬‫א‬ I R ‫א‬ I T ‫א‬‫א‬  W‫א‬‫א‬  IT  IC  θ  IR  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٥J ١٣F  I T 2 = I R 2 + I C 2      W،‫א‬       E٣١J ١٣F  W 2 2           E٣٢J ١٣F 2 2           E٣٣J ١٣F 2 2           E٣٤J ١٣F  IT = I R + IC  I R = IT − IC  IC = IT − I R   - ٢٩٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Ohm's Law‫א‬‫א‬‫א‬‫א‬ ٥J ٨J ١٣  W‫א‬،،‫א‬‫א‬  C  I   R  ‫א‬‫א‬RC‫א‬E٢٦J ١٣F  V = I *Z        V Z V Z= I               I=  W     E٣٥J ١٣F      E٣٦J ١٣F      E٣٧J ١٣F  W‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬،   ‫א‬‫א‬‫א‬E٢٧J ١٣F   ‫א‬ RC ‫א‬ RC ‫א‬‫א‬٦J ٨J ١٣ Conversion From Parallel to Series Form  RC ‫א‬  ‫א‬‫א‬ RC ‫א‬،‫א‬ ‫א‬‫א‬،‫א‬‫א‬ RC ‫א‬‫א‬‫א‬ RC ‫א‬،‫א‬‫א‬  ،‫א‬‫א‬‫א‬  RC ‫א‬  ‫א‬ RC ‫א‬  W‫א‬‫א‬‫א‬‫א‬ - ٣٠٠ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Ceq  Req   VS VS  C R    ‫א‬‫א‬RC‫א‬‫א‬‫א‬‫א‬E٢٨J ١٣F     W C eq  X ceq  Req ‫א‬‫א‬‫א‬‫א‬‫א‬ Req = Z . cos θ            E٣٨J ١٣F  x ceq = Z . sin θ            E٣٩J ١٣F  ⇒ C eq = 1 2πFZ . sin θ           E٤٠J ١٣F   E٥J ١٣F  W‫א‬‫א‬‫א‬   VS(rms)=10v R 1k F=10kHz   E٥J ١٣F‫א‬‫א‬‫א‬E٢٩J ١٣F  XC = Z= R2 + X C 2 - ٣٠١ -  X C ‫א‬‫א‬ K Z ‫א‬ K  1 = 1.6kΩ 2π .F .C R. X C  C=0.01uF = 843.5Ω  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    I R ‫א‬‫א‬‫א‬ I R ( rms ) = V S ( rms ) R = 10mA I C ‫א‬‫א‬‫א‬ I C ( rms ) = = XC K  = 6.25mA  I T ‫א‬‫א‬ K  (a )I T ( rms ) = (b )I Trms V S ( rms ) K  I R2 ( rms ) + I C2 ( rms ) = 11.8mA V S ( rms ) Z = 10 = 11.8mA 843.5 θ ‫א‬‫א‬ K ⎞ ⎟⎟ = 32 0 ⎠ ⎛I ⎞ (b )θ = tan −1 ⎜⎜ C ( rms ) ⎟⎟ = 32 0 ⎝ I R ( rms ) ⎠ ⎛ R ⎝ XC  (a )θ = tan −1 ⎜⎜   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ RC ‫א‬‫א‬ K   Req = Z . cos θ = 843.5 * cos 32 o = 715.3Ω X Ceq = Z . sin θ = 843.5 * sin 32 o = 452.3Ω  ⇒ C eq = 1 = 0.035µF 2πF * X Ceq   Req=7153  VS Ceq=0.035uF    - ٣٠٢ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬Summary ‫ﻋﻠﻰ اﻟﺘﻮازي‬  2 IT = I R + IC  Z= ‫داﺋﺮة‬ ‫א‬ 2 R. X C R2 + X C ⎛ XC ⎞ ⎟ ⎝ R ⎠ ‫ﻋﻠﻰ اﻟﺘﻮاﻟﻲ‬ RC 2  2 V S = V R + VC ‫א‬  θ = tan −1 ⎜  ⎛I θ = tan ⎜⎜ C ⎝ IR −1 ⎞ ⎟⎟ ⎠ 2 ‫داﺋﺮة‬ ‫א‬ RC Z = R2 + X C ⎛ XC ⎞ ⎟ ⎝ R ⎠  2 ‫א‬ θ = tan −1 ⎜ ‫א‬‫א‬  ⎛V θ = tan ⎜⎜ C ⎝ VR −1 ⎞ ⎟⎟ ⎠ ‫א‬‫א‬  - ٣٠٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Series-Parallel RC Circuits‫א‬‫א‬‫א‬E‫א‬J ‫א‬F‫א‬‫א‬٩J ١٣  K‫א‬‫א‬‫א‬‫א‬‫א‬  E٦J ١٣F  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  R1=1k  VS(rms)=10v  C1=0.1uF R2 C2=0.05uF  680 F=5kHz   E٦J ١٣F‫א‬‫א‬‫א‬E٣٠J ١٣F  K‫א‬‫א‬ (1   ‫א‬‫א‬ (2 I ‫א‬ VS ‫א‬ θ ‫א‬‫א‬ (3   ‫א‬  W‫א‬‫א‬W 1 = 318Ω 2πF .C1 1 = = 637Ω 2πF .C 2  X C1 =  X C2  W‫א‬E‫א‬‫א‬ RC F‫א‬‫א‬‫א‬‫א‬ RC ‫א‬‫א‬W Ceq Req R C - ٣٠٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    R2 * C 2  Z2 =  θ = tan −1 ⎜⎜ ⎛ R2 ⎝ XC2   2 R2 + X C2 2 = 465Ω W‫א‬‫א‬ ⎞ ⎟ = 46.9 o W‫א‬‫א‬‫א‬ ⎟ ⎠ ⇒ Req = Z 2 cos θ = 318Ω W‫א‬‫א‬ X Ceq = Z 2 sin θ = 340Ω W‫א‬‫א‬‫א‬  W،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Xceq Req R1 VS   Xc1  F    K‫א‬‫א‬‫א‬     K‫א‬‫א‬،‫א‬‫א‬   RT = R1 + Req = 1.32kΩ W‫א‬‫א‬ X CT = X C1 + X Ceq = 658Ω W‫א‬‫א‬  Rt=1.32k  VS  Xct=658 ohm       K‫א‬‫א‬ RC ‫א‬‫א‬J ‫א‬‫א‬ - ٣٠٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     2 Z T ‫א‬‫א‬ K I T ‫א‬‫א‬ K  θ ‫א‬‫א‬ K  2 Z T = RT + X CT = 1.47kΩ  W  I rms =  V Srms 10V = = 6.8mA ZT 1.47 kΩ θ = tan −1 X CT = 26.50 o RT  E٧J ١٣F  W‫א‬‫א‬‫א‬  R1 VS  C1 F R2 V2 V1  E٧J ١٣F‫א‬‫א‬‫א‬E٣١J ١٣F    V 1rms= I rms * Z 1  ⇒ V1rms = (6.8mA) * (1.05kΩ ) = 7.13V 2    Z 1  C1  R1 ‫א‬K  I rms = 6.8mA ‫א‬‫א‬ 2 Z 1 = R1 + X C! = 1050Ω  W Z 2 ‫א‬ V2 ‫א‬K   C2  V2 rms = I rms * Z 2 = (6.8mA) * (465Ω ) = 3.16V  V Rrms = I rms * R1 = 6.8V VCrms = I rms * X C1 = 2.16V - ٣٠٦ - C1 ‫א‬ R1 ‫א‬K  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     C 2 ‫א‬ R2 ‫א‬K V2 3.16 = = 4.64mA R 2 680 V 3.16 = 2 = = 4.9mA X C2 340  I R2 =  IC2  Power in RC Circuits‫א‬‫א‬‫א‬‫א‬١٠J ١٣ Power Triangle‫א‬١J ١٠J ١٣ ،‫א‬‫א‬ RC ‫א‬‫א‬ RC ‫א‬،  ‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬ RC ‫א‬‫א‬  W‫א‬،‫א‬‫א‬ RC ‫א‬‫א‬‫א‬ RC ‫א‬  C  R Vr VS   Vc    ‫א‬‫א‬RC‫א‬E٣٢J ١٣F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W I rms ‫א‬‫א‬   I rms ‫א‬‫א‬E٣٣J ١٣F  W  K‫א‬‫א‬‫א‬‫א‬ VR C I rms rms  K‫א‬‫א‬ VC C I rms rms  KApparent Power‫א‬‫א‬ VS C I rms rms - ٣٠٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      W‫א‬،‫א‬   ‫א‬‫א‬RC‫א‬‫א‬E٣٤J ١٣F   Powers Relationship‫א‬٢J ١٠J ١٣  WApparent Power‫א‬‫א‬  Pa = V Srms * I rms =        E٤١J ١٣F WTrue Power‫א‬‫א‬       E٤٢J ١٣F Pr = Pa . sin θ       E٤٣J ١٣F     Ptrue = Pa . cos θ  2 V Srms 2 = I rms *Z  Z  WReactive Power‫א‬‫א‬   ‫א‬‫א‬٣J ١٠J ١٣  (W )  Watt W‫א‬‫א‬  (VAR )  Volt − Ampere − Re active W‫א‬‫א‬  (VA)  Vott − Ampere W‫א‬‫א‬  The Significance of apparent Power‫א‬‫א‬٤J ١٠J ١٣ ،EFApparent Power‫א‬‫א‬ ‫א‬  ‫א‬‫א‬K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ E‫א‬‫א‬F‫א‬‫א‬‫א‬ ‫א‬‫א‬K ‫א‬ ‫א‬  ‫א‬‫א‬،  K - ٣٠٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬       ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  PF : thePowerFactor ‫א‬،‫א‬‫א‬   EThe Power Factor (PF‫א‬٥J ١٠J ١٣ ،‫א‬‫א‬‫א‬،Power Factor‫א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،PF‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬   PF = Ptrue = cos θ Pa PF = cos θ                  E٤٤J ١٣F  W E٤٥J ١٣F    K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ W θ   ‫א‬،‫א‬‫א‬ θ ‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬    W‫א‬‫א‬‫א‬‫א‬  ‫א‬W  K θ = 0 o ،‫א‬‫א‬‫א‬،‫א‬‫א‬  cos(0 o ) = 1 ، sin(0 o ) = 0  Ptrue = Pa = V S ( rms ) * I rms    W Pr = 0  PF = 1 W ،  - ٣٠٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬W  K θ = 90 o ،٩٠‫א‬‫א‬،‫א‬‫א‬‫א‬    cos(90 o ) = 0 ، sin(90 o ) = 1   W Ptrue = 0 Pr = Pa = V S ( rms ) * I rms  PF = 0 W،  RC‫א‬W K 0 < PF < 1 ، ‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬   E٨J ١٣F  ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬   E٨J ١٣F‫א‬‫א‬‫א‬E٣٥J ١٣F  XC =  Z =  Pa = 1 = 3.18kΩ 2πF .C R 2 + X 2 C = 3 . 33 k Ω ‫א‬  2 V srms = 67.5 * 10 −3 VA = 67.5mVA Z   - ٣١٠ - ⎛ XC ⎞ ⎟ = 72.5 o W‫א‬‫א‬ ⎝ R ⎠ θ = tan −1 ⎜ Ptrue = Pa . cos θ = 20.3mW  W‫א‬‫א‬ PF = cos θ = 0.301 W‫א‬  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Summary‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١  KEE VR and I R )are in Phase) ‫א‬Leads‫א‬‫א‬‫א‬، K٢  KEPhase Shift)‫א‬‫א‬‫א‬‫א‬، 90 o  E‫א‬F‫א‬‫א‬‫א‬‫א‬‫ א‬K٣ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫ א‬K٤  W‫א‬‫א‬‫א‬‫א‬‫א‬  Ptrue = 0 ،‫א‬‫א‬‫א‬‫א‬ K٥ W‫א‬‫א‬‫א‬ Pr = Vrms * I rms  W‫א‬‫א‬‫א‬‫א‬‫ א‬K٦  CT = 1 1 1 1 + + .... C1 C 2 CN  W،   X CT = X C! + X C2 + X C N  C T = C1 + C 2 + L + C N W‫א‬‫א‬‫א‬‫א‬‫ א‬K٧ X CT = 1 1 1 1 + + .... X C! X C 2 X CN  - ٣١١ -  W،  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    W،‫א‬‫א‬‫א‬‫א‬ K٨  Z = R2 + XC ⎛ VC ⎝ VR  θ = tan −1 ⎜⎜ 2 ⎞ ⎟⎟ ⎠ 2 VS = VR + VC 2 W،‫א‬‫א‬‫א‬‫א‬‫א‬ K٩ R *C  Z=  θ = tan −1 ⎜⎜  2 R2 + X C ⎛ IC ⎝ IR ⎞ ⎟⎟ ⎠ 2 IT = I R + IC 2 W‫א‬‫א‬‫א‬‫א‬ RC ‫א‬‫א‬ RC ‫א‬ K١٠   Req = Z . cos θ x ceq = Z . sin θ ⇒ C eq = 1 2πFZ . sin θ   ‫א‬‫א‬‫א‬‫א‬Summary  K١١ ‫א‬‫א‬ RC ‫א‬  2 IT = I R + IC  Z= 2 ‫א‬ R. X C R + XC 2 ‫א‬‫א‬ RC ‫א‬ 2  2 V S = V R + VC ‫א‬  ⎛ XC ⎞ ⎟ ⎝ R ⎠ ‫א‬‫א‬ −1 ⎛ I C ⎞ θ = tan ⎜⎜ ⎟⎟ ⎝ IR ⎠ θ = tan −1 ⎜  - ٣١٢ - ‫א‬ Z = R2 + X C 2 ‫א‬ ⎛ XC ⎞ ⎟ ⎝ R ⎠ ‫א‬‫א‬ −1 ⎛ VC ⎞ θ = tan ⎜⎜ ⎟⎟ ⎝ VR ⎠ θ = tan −1 ⎜  2   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬ K١ (b) (a) C=0.047µF C1   C2  1H2  F= 1kH2  C1=10µF  C2=15µF  (c)  60H2    C1=1µF C2=1µF  W‫א‬‫א‬‫א‬ K٢ Irms= ImA   C=0.0047µF   F= 10kH2   ‫؟‬‫א‬‫א‬‫א‬ • ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  ‫؟‬‫א‬‫א‬‫א‬ • - ٣١٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٣  W‫א‬‫א‬، I Tavg ‫א‬‫א‬ I Trms ‫א‬‫א‬ K٤  W‫א‬‫א‬‫א‬‫א‬ K٥  - ٣١٤ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    W‫א‬‫א‬‫א‬ K٦  (  I : C ‫א‬‫א‬‫א‬ ( 2  I : C ‫א‬‫א‬‫א‬ ( 3  I : R ‫א‬‫א‬‫א‬ ( 4  I T ‫א‬‫א‬ o 1 o 1 c1 o 2 C2 o R W‫א‬‫א‬ RC ‫א‬‫א‬‫א‬‫א‬ K٧  K٨ V R2 , V R1 , θ , I T , VC , V R3   W‫א‬‫א‬‫א‬ I 2 , I 1 ،‫א‬‫א‬ I T  K٩  ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬،  - ٣١٥ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Ptrue   Pr  W RC ‫א‬ K١٠ = 2W W TruePower ‫א‬‫א‬ = 3.5V . A.R W Re activePower ‫א‬‫א‬  ‫؟‬ ApperentPower  Pr ‫א‬‫א‬‫א‬ ،Power Factor‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ K١١  W‫א‬‫א‬   - ٣١٦ -  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ١٤  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٤ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬ W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   - ٣١٧ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction١J ١٤ ، ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ E ‫א‬‫א‬F‫א‬  ‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬،Open Circuit‫א‬‫א‬  K‫א‬‫א‬ ‫א‬E‫א‬F‫א‬ ‫א‬،‫א‬‫א‬‫א‬ ‫א‬ ‫א‬KE ‫א‬ ‫א‬‫א‬F‫א‬  K‫א‬،Short Circuit‫א‬‫א‬   Inductive Reactance X L ‫א‬‫א‬٢J ١٤  W‫א‬‫א‬، X L ‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬، ‫א‬‫א‬  W‫א‬،‫א‬‫א‬‫א‬ F  N  I    L     ‫א‬‫א‬‫א‬‫א‬E١J ١٤F - ٣١٨ -   ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     K‫א‬‫א‬‫א‬  ‫א؟‬K‫א‬،F‫א‬‫א‬   ‫א‬،‫א‬ ‫א‬‫א‬    ‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  ‫א‬  K‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬، X L  W ↔F ‫א‬ X L ‫א‬‫א‬‫א‬ K١  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،Inductive Reactance X L ‫א‬‫א‬‫א‬‫א‬ K٢  K Ohm(Ω) ‫א‬   ‫א‬‫א‬ ‫א‬‫א‬‫א‬  W‫א‬،‫א‬‫א‬   F N  I     L     ‫א‬‫א‬‫א‬‫א‬E٢J ١٤F  - ٣١٩ - F0   ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬K ‫א‬‫א‬‫א‬    ‫א‬‫א‬   ،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ K‫א‬ X L ‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬ ‫א‬،‫א‬،‫א‬،  X L = 2πF .L   W،Inductive Reactance Formula   E١J ١٤F   E١J ١٤F  W‫א‬‫א‬‫א‬  I   L 5mH Vs F=1kHz     E١J ١٤F‫א‬‫א‬‫א‬E٣J ١٤F   X L ‫א‬‫א‬  ‫א‬  X L = 2πF .L = 2π *1*10 3 * 5 *10 −3 = 31.4Ω   Ohm's Law in Inductive AC Circuits‫א‬‫א‬‫א‬‫א‬٣J ١٤ ‫א‬، ،‫א‬‫א‬ ‫א‬ K  ‫א‬،E٤J ١٤F‫א‬  K Henry‫א‬‫א‬ - ٣٢٠ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   I  L   XL    ‫א‬‫א‬‫א‬‫א‬E٤J ١٤F  ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬  ،  V = I . X L   I=   W، V  XL V X L =  I   E٢J ١٤F   E٣J ١٤F   E٤J ١٤F  W‫א‬‫א‬‫א‬‫א‬      XL   ‫א‬E٥J ١٤F     Peak  RMS ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K Peak − to − Peak  - ٣٢١ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٢J ١٤F   Vs F=10k Hz  W‫א‬‫א‬‫א‬ I  L 100mH     E٢J ١٤F‫א‬‫א‬‫א‬E٦J ١٤F  ‫؟‬‫א‬‫א‬  ‫א‬ X L = 2πF .L = 6.3kΩ  I rms = V srms = 796µA X1 I avg = 0.9 I rms = 716.4µA.   ‫א‬‫א‬‫א‬‫א‬٤J ١٤ Current & Voltage Relationship in Inductive Circuits ‫א‬‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬،KEE VR and I R )are in Phase)،‫א‬  KEPhase Shift)‫א‬‫א‬‫א‬‫א‬، 90 o ‫א‬Lags   ‫א‬‫א‬‫א‬E٧J ١٤F - ٣٢٢ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  K 90 0 ‫א‬EF‫א‬  Power in an Inductor ‫א‬‫א‬‫א‬٥J ١٤ ‫א‬DC‫א‬ ‫א‬‫א‬‫א‬، ،‫א‬‫א‬‫א‬‫א‬K‫א‬، P = V .I ‫א‬ ‫א‬،‫א‬‫א‬‫א‬K    W‫א‬‫א‬  Instantaneous Power‫א‬‫ א‬١-٥-١٣ E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬E٨J ١٤F     K‫א‬‫א‬‫א‬‫ א‬K١ K‫א‬‫א‬‫א‬‫ א‬K٢ K‫א‬‫א‬‫א‬‫ א‬K٣ ‫א‬‫א‬، ‫א‬‫א‬‫א‬ ‫א‬‫א‬ K٤ W - ٣٢٣ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     K‫א‬‫ א‬Ka K‫א‬‫ א‬Kb ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ K٥  W  K‫א‬‫ א‬Ka  K‫א‬‫ א‬Kb  True Power Ptrue ‫א‬‫א‬٢J ٥J ١٤ ‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬ Ptrue = 0         W‫א‬‫א‬‫א‬،‫א‬       E٥J ١٤F ‫א‬‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬ ‫א‬K RW ‫א‬  2 Ptrue = I rms RW         W،      Pr Reactive Power‫א‬‫א‬ E٦J ١٤F  ٣-٥-١٤ ،‫א‬ ‫א‬‫א‬‫א‬  Pr = Vrms * I rms        2 Vrms Pr = XL       2 Pr = I rms * XL      W‫א‬‫א‬‫א‬      E٧J ١٤F       E٨J ١٤F       E٩J ١٤F  K‫א‬‫א‬‫א‬W Vrms W  K‫א‬‫א‬‫א‬W I rms   K(VAR) Volt- Ampere – ReactiveW‫א‬‫א‬‫א‬‫א‬ Pr  - ٣٢٤ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٣J ١٤F  W‫א‬‫א‬‫א‬ I   L=10mH  Vrms=10V F=1k Hz    E٣J ١٤F‫א‬‫א‬‫א‬E٩J ١٤F  K‫א‬‫א‬  ‫א‬ 2  V Pr = rms XL  V X L = 2πF .L = 62.8Ω ⇒ Pr = rms = 1.59VAR XL 2 ‫א‬‫א‬K RW  E٤J ١٤F = 5Ω ،‫א‬‫א‬،‫א‬  ‫؟‬ Ptrue ‫א‬   ‫א‬  E‫א‬F‫א‬‫א‬‫א‬‫א‬  I rms = Vrms = 159mA XL  W‫א‬‫א‬  2 ⇒ Ptrue = I rms * RW = 126mw   - ٣٢٥ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Series & Parallel Inductive AC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٦J ١٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬ W  Series Inductors‫א‬‫א‬‫א‬١J ٦J ١٤  W‫א‬‫א‬‫א‬‫א‬‫א‬ L1 L2 Ln    ‫א‬‫א‬‫א‬‫א‬E١٠J ١٤F  W،‫א‬‫א‬‫א‬  LT = L1 + L2 .... + L N   X LT = X L1 + X L2 + ... X LN        E١٠J ١٤F  W‫א‬‫א‬‫א‬،      E١١J ١٤F    Parallel Inductors‫א‬‫א‬‫א‬٢J ٦J ١٤  W‫א‬‫א‬‫א‬‫א‬‫א‬   L1 L2 Ln     ‫א‬‫א‬‫א‬‫א‬E١١J ١٤F - ٣٢٦ -   ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     LT =  W،‫א‬‫א‬‫א‬ 1 1 1 1 + + .... L1 L2 LN X LT =   1 1 1 1 + + ... + X L1 X L 2 X LN          E١٢J ١٤F  W،     - ٣٢٧ -      E١٣J ١٤F  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     WSummary‫א‬‫א‬‫א‬‫א‬‫א‬ InductorsE‫א‬F‫א‬ Capacitors‫א‬  Inductance‫א‬  L= Capacitance‫א‬ N µ. A l 2  C= W = 1 2 LI 2   X L = 2π .F .L V = I .X L ‫א‬‫א‬‫א‬‫א‬  90 o ‫א‬‫א‬  1 CV 2 2 XC = 1 2π .F .C  V = I .X C ‫א‬‫א‬‫א‬‫א‬ 90 o ‫א‬‫א‬   ‫א‬‫א‬K  ‫א‬‫א‬  W =  K  K  ) Capacitive Reactance‫א‬‫א‬ Inductive Reactance‫א‬‫א‬  ( A * ε r * 8.85 * 10 −12 d  ‫א‬‫א‬K  ‫א‬‫א‬    LT = L1 + L2 + ...LN X LT = X L1 + X L2 + ... + X LN  - ٣٢٨ - CT = 1 1 1 1 + + ... C1 C 2 CN X CT = X C1+ X C2 + ..... X C N  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    InductorsE‫א‬F‫א‬ Capacitors‫א‬  ‫א‬‫א‬  ‫א‬‫א‬   X LT  1 LT = 1 1 1 + + ... + L1 L2 LN 1 = 1 1 1 + + ... + X L1 X L2 X LN    ‫א‬‫א‬K  ‫א‬‫א‬ LT = L1 + L2   X LT = X L1 + X L2    ‫א‬‫א‬ LT =  CT = X CT = X C1 + X C2 CT = C1 + C 2  X L1 . X L2 X l1 + X L2 X CT =   LT = N .L X LT = N . X L  L‫א‬‫א‬‫א‬  X C1 . X C2 X C1 + X C2 C‫א‬‫א‬‫א‬ L‫א‬‫א‬‫א‬  C1C 2 C1 + C 2  ‫א‬‫א‬ L1 .L2 L1 + L2 X LT = CT = C1 + C 2 + .....C N 1 X CT = 1 1 1 + + ... X c1 X C2 X CN CT = C N X CT = N . X C C‫א‬‫א‬‫א‬K L LT = N XL X LT N  CT = N .C X CT = XC N  - ٣٢٩ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Series RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١٤  Characteristics of RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٧J ١٤  W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  IL R VR XL VL      ‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ١٤F    ‫א‬‫א‬‫א‬‫א‬‫א‬ K V L ‫א‬‫א‬ I L  ‫א‬‫א‬، ‫א‬ VR ‫א‬ I R   ‫א‬‫א‬‫א‬، ‫א‬  K‫א‬‫א‬‫א‬‫א‬ ، 90 o ‫א‬‫א‬ V L  I L ،‫א‬ ‫א‬ ‫א‬K 90 o ‫א‬‫א‬ V L ‫א‬ VR ‫א‬‫א‬  W‫א‬ 90 o ‫א‬‫א‬،‫א‬ VL  VS   θ  I  VR  ‫א‬‫א‬E١٣J ١٤F  K V L + V R ‫א‬‫א‬ V L  VR      K V L  VR ‫א‬‫א‬‫א‬ - ٣٣٠ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     VS  I ‫א‬  ، θ  VS  VR   ‫א‬ ‫א‬‫א‬K ‫א‬‫א‬ ‫א‬ VR  I  θ  ،Phase angle‫א‬‫א‬ θ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K θ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬RL‫א‬ . θ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ RL ‫א‬   Impedance Z‫ א‬٢-٧-١٤ ‫א‬، ‫א‬‫א‬‫א‬‫א‬  ‫א‬،  ‫א‬، RT ‫א‬E ‫א‬F‫א‬‫א‬‫א‬  F ‫א‬‫א‬  ، LT ‫א‬‫א‬‫א‬‫א‬  KOhmZ‫א‬  W‫א‬Series R – L ‫א‬‫א‬‫א‬‫א‬  VS = I.X S VL = I.X L Z XL θ θ R VR = I.R Z 2 = R2 + X L  2  Z = R2 + X L  2    ‫א‬E١٤J ١٤F    WPythagoras‫א‬‫א‬             E١٤J ١٤F       E١٥J ١٤F  W‫א‬‫א‬RL‫א‬ - ٣٣١ -   ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     θ Phase Angle‫א‬‫א‬ ٣-٧-١٤ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ θ  VS VS VL θ XL θ VR    R  ‫א‬‫א‬‫א‬‫א‬E١٥J ١٤F  W  ⎛ XL ⎞ −1 ⎛ V ⎟ and  θ = tan ⎜⎜ L ⎝ R ⎠ ⎝ VR θ = tan −1 ⎜ ⎞ ⎟⎟  ⎠      E١٦J ١٤F   ،‫א‬‫א‬ θ ‫א‬‫א‬‫א‬E tan θ F θ ‫א‬‫א‬  W  tan θ = VL VR E١٧J ١٤F  (tan ) ‫א‬‫א‬‫א‬‫א‬‫א‬ (tan −1 ) ‫א‬‫א‬W  K VL VR ⎛ VL ⎝ VR ‫א‬‫א‬‫א‬ θ = tan −1 ⎜⎜ ⎞ ⎟⎟ ‫א‬ ⎠  Voltages Relationships‫א‬‫א‬RL‫א‬‫א‬‫ א‬٤-٧-١٤  V L ‫א‬  ‫א‬ VR ‫א‬‫א‬ VS ‫א‬  W‫א‬‫א‬ VL VS θ VR  ‫א‬‫א‬RL‫א‬‫א‬E١٦J ١٤F - ٣٣٢ -     ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬‫א‬‫א‬  VS  θ  VR  ‫א‬‫א‬RL‫א‬‫א‬E١٧J ١٤F     K‫א‬‫א‬  Vs = V R + V L  VS = VR + VL  VR = VS − VL  VL = VS − VR 2 2 2    WPythagoras   E١٨J ١٤F  W‫א‬‫א‬‫א‬‫א‬ 2 2    E١٩J ١٤F 2 2    E٢٠J ١٤F 2 2    E٢١J ١٤F  Ohm's Law‫א‬‫א‬‫א‬‫א‬ ٥J ٧J ١٤ ،،‫א‬‫א‬  W‫א‬  I R VR  XL VL  ‫א‬‫א‬RL‫א‬E١٨J ١٤F  W‫א‬‫א‬ VR ‫א‬‫א‬‫א‬‫א‬  V R = I .R       - ٣٣٣ -      E٢٢J ١٤F  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ، X L ‫א‬‫א‬، V L   ‫א‬‫א‬ VL = I .X L        W V L ‫א‬‫א‬‫א‬‫א‬       E٢٣J ١٤F ،E ‫א‬‫א‬F V ‫א‬ ‫א‬‫א‬‫א‬‫א‬  V = I .Z   V Z V Z= I I=         W‫א‬‫א‬‫א‬ RL ‫א‬Z‫א‬         E٢٤J ١٤F          E٢٥J ١٤F          E٢٦J ١٤F  W‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬،   ‫א‬E١٩J ١٤F   Frequency Effect on RL ‫א‬‫א‬‫א‬‫א‬ ٦-٧-١٤ K ‫א‬،‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  W‫א‬‫א‬‫א‬  WK ( X L = 2πFL ) ، X L ‫א‬‫א‬ F ‫א‬‫א‬ K١ ⎛⎜ Z = R 2 + X 2 ⎞⎟ W‫א‬ ⇐ L ⎝ ⎠ KE‫א‬‫א‬F I = V W‫⇐ א‬ Z      KVL  VR ‫א‬ ⇐  K (VS 2 = V R 2 + V L 2 ) V L ‫א‬ ⇐ ↑ V L ↓ V R ⇐↑ I  ↓ Z ⇐↓ X L ⇐ F  - ٣٣٤ - K٢   ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬  ↑ VL  ↓ VR  ↓ I  ↑ Z  ↑ X L WF‫א‬ ↑ VL  ↓ VR  ↓ I  ↑ Z  ↑ X L WF‫א‬   E٥J ١٤F I= 200µA R L  W‫א‬‫א‬‫א‬  10 K Ω 100 mH VS VR  VL  F =10KHZ  E٥J ١٤F‫א‬‫א‬‫א‬E٢٠J ١٤F  X L ‫א‬‫א‬ X L = 2πFL = 6.28kΩ K  ‫ א‬K   2 Z = R 2 + X L = 11.8kΩ ‫א‬ K  V R = I .R = 2V  ‫א‬ K  V L = I * X L = 1.256V  ‫א‬ K 2 2 (a)V S = V R + V L = 2.36V (b)V S = I .Z = 2.36V  ‫א‬‫א‬ K ⎛ XL ⎝ R ⎞ ⎟ = 32 0 ⎠ ⎛ VL ⎝ VR ⎞ ⎟⎟ = 32 0 ⎠ θ = tan −1 ⎜  θ = tan −1 ⎜⎜ - ٣٣٥ -   ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Parallel RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١٤  Characteristics of RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ١٤  W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ IT IL IR R Vs    L    ‫א‬‫א‬RL‫א‬E٢١J ١٤F  W V L = V R = V S  • ‫א‬ VR  I R • K 90 o ‫א‬‫א‬ I R  I L • K θ ‫א‬‫א‬ I L ‫א‬‫• א‬ IR Vs θ  IT RL      ‫א‬‫א‬RL‫א‬‫א‬E٢٢J ١٤F  Impedance Z‫ א‬٢-٨-١٤ ‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬، ،‫א‬‫א‬KOhmZ‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٣٣٦ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     IR= VR/R θ   IT= VS/Z   IL= VL/XL  ‫א‬‫א‬RL‫א‬‫א‬E٢٣J ١٤F  IR = VR R   W   E٢٧J ١٤F ‫א‬،Parallel R – L ‫א‬‫א‬‫א‬‫א‬  W‫א‬Admittance triangle‫א‬‫א‬، VS 1/R θ = VR = VL   1/Z    1/XL  ‫א‬‫א‬RL‫א‬‫א‬E٢٤J ١٤F  W‫א‬‫א‬‫א‬‫א‬،‫א‬  1/R θ 1/Z  1/XL   ‫א‬E٢٥J ١٤F   ‫א‬،‫א‬،‫א‬admittance‫א‬،  K‫א‬‫א‬، 1 ، Z 1 XC ، 1  R  - ٣٣٧ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Z‫א‬‫א‬ ،‫א‬  W  1 1 1 = 2 + 2 2 Z R XL  X L2 + R 2 1 = ⇒Z = Z 2 R 2 * X L2  RX L R 2 + X L2    E٢٨J ١٤F   E٢٩J ١٤F  θ Phase Angle‫א‬‫א‬ ٣-٨-١٤ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ θ   W‫א‬‫א‬  IR θ  1/R θ IL 1/XL 1/Z  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٦J ١٤F  ⎛I ⎛ R ⎞ ⎟⎟ and  θ = tan −1 ⎜⎜ L ⎝ XL ⎠ ⎝ IR θ = tan −1 ⎜⎜ ⎞ ⎟⎟  ⎠        W   E٣٠J ١٤F   ،‫א‬‫א‬ θ ‫א‬‫א‬‫א‬E tan θ F θ ‫א‬‫א‬  W  tan θ = IL IR E٣١J ١٤F  (tan ) ‫א‬‫א‬‫א‬‫א‬‫א‬ (tan −1 ) ‫א‬‫א‬W  K IL IR ⎛ IL ⎝ IR ‫א‬‫א‬‫א‬ θ = tan −1 ⎜⎜ ⎞ ⎟⎟ ‫א‬ ⎠  - ٣٣٨ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Currents Relationships‫א‬‫א‬RL‫א‬‫א‬‫א‬‫ א‬٤J ٨J ١٤  I L ‫א‬‫א‬‫א‬ I R ‫א‬ I T ‫א‬‫א‬  W‫א‬‫א‬  IR  θ IL  IT  ‫א‬‫א‬RL‫א‬‫א‬‫א‬‫א‬E٢٧J ١٤F   2 2 IT = I R + I L 2 2   2  2    W،‫א‬  2 2 IT = I R + I L ⇒ I R = IT − I L ⇒ I L = IT − I R 2          E٣٢J ١٤F  W  E٣٣J ١٤F Ohm's Law‫א‬‫א‬‫א‬‫א‬ ٥J ٨J ١٤ ،،‫א‬‫א‬  W‫א‬ R  XL  Z   I   V   ‫א‬‫א‬RL‫א‬E٢٨J ١٤F  V = I *Z       - ٣٣٩ -      W  E٣٤J ١٤F  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬‫א‬‫א‬  I= V V ⇒Z = Z I           E٣٥J ١٤F  W‫א‬‫א‬‫א‬‫א‬،   ‫א‬E٢٩J ١٤F   ‫א‬ RL ‫א‬ RL ‫א‬‫א‬٦J ٨J ١٤ KConversion From Parallel to Series Form  RL ‫א‬  ‫א‬‫א‬ RL ‫א‬،‫א‬ ‫א‬‫א‬،‫א‬‫א‬ RL ‫א‬‫א‬‫א‬ RL ‫א‬،‫א‬‫א‬  ،‫א‬‫א‬‫א‬  RL ‫א‬  ‫א‬ RL ‫א‬  W‫א‬‫א‬‫א‬‫א‬  Vs R eq R XL VS  ‫א‬‫א‬RL‫א‬‫א‬‫א‬‫א‬E٣٠J ١٤F XL eq      ،‫א‬‫א‬‫א‬‫א‬‫א‬   Req = Z cos θ  X Leq = Z sin θ ⇒ Leq = X Leq 2πF = Z . sin θ 2πF  W‫א‬‫א‬‫א‬ X Leq  Req     E٣٦J ١٤F   E٣٧J ١٤F  - ٣٤٠ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٦J ١٤F  W‫א‬‫א‬‫א‬ IT IL IR R Vs  L 2.2 KΩ 10 v   150mH    E٦J ١٤F‫א‬‫א‬‫א‬E٣١J ١٤F  X L ‫א‬‫א‬ K Z ‫א‬ K  I R ‫א‬‫א‬‫א‬ K   X L = 2π .F .L = 1.41kΩ Z= RX L I R ( rms ) = V S ( rms ) R = 1.19kΩ 2 R2 + X L = 4.54mA I L ‫א‬‫א‬‫א‬ I L ( rms ) = = XL = 7.1mA  I T ‫א‬‫א‬ K  (a )I T ( rms ) =  (b )I Trms V S ( rms ) I R2 ( rms ) + I L2( rms ) = 8.42mA V S ( rms ) Z = 8.42mA θ ‫א‬‫א‬ ⎛ R ⎝ XL ⎞ ⎟⎟ = 57.3 0 ⎠ ⎛I ⎞ (b )θ = tan −1 ⎜⎜ L ( rms ) ⎟⎟ = 57.3 0 ⎝ I R ( rms ) ⎠  (a )θ = tan −1 ⎜⎜  K  - ٣٤١ - K  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ RL ‫א‬‫א‬ K  XL eq R eq Vs       Req = Z . cos θ = 643Ω And X Leq = Z . sin θ = 1kΩ ⇒ Leq = X Leq 2πF = 106.25mH   Series -Parallel RL Circuits‫א‬‫א‬‫א‬E‫א‬J ‫א‬F‫א‬‫א‬٩J ١٤  K‫א‬‫א‬‫א‬‫א‬‫א‬    W‫א‬‫א‬‫א‬  IT ١R 4.7 KΩ Vs  L1 mH٢٥٠ R2 KΩ٣٫٣ 10 v F = 5KHZ  E٧J ١٤F‫א‬‫א‬‫א‬E٣٢J ١٤F L1 mH١٠٠     K Z T ‫א‬‫א‬ (1    K I T ‫א‬‫א‬ (2 I ‫א‬ VS ‫א‬ θ ‫א‬‫א‬ (3 X L1 = 2πFL1 = 7.85kΩ X L2 = 2πFL2 = 3.14kΩ - ٣٤٢ -  ‫א‬  W‫א‬‫א‬W  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W  R eq XL eq R2 2  XL2  XL   Z2 =   K‫א‬‫א‬‫א‬‫א‬ R2 . X L 2 2 R2 + X L ⎛ R2 ⎜ XL ⎝ 2 θ 2 = tan −1 ⎜  2 = 2.28kΩ ⎞ ⎟ = 46.4 0 ⎟ ⎠ ⎧ Req = Z 2 cos θ 2 = 1.57kΩ  ⇒ ⎪⎨ ⎪⎩ X Leq = Z 2 . sin θ 2 = 1.65kΩ  W،‫א‬‫א‬‫א‬‫א‬  Vs XL 1 R1 R eq XL eq      ‫א‬‫א‬  ، RT RT = R1 + Req = 6.27kΩ  ‫א‬‫א‬‫א‬  X LT = X L1 + X Leq = 9.5kΩ = 6.27 kΩ ‫א‬‫א‬ X L = 9.5kΩ ‫א‬‫א‬‫א‬ T  W 2 2 Z T = RT + X LT = 11.4kΩ  ⎛ X LT ⎞ ⎟ = 56.6 o ⎟ ⎝ RT ⎠ θ = tan −1 ⎜⎜ IT = VS = 877 µA. ZT - ٣٤٣ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Power in RL Circuits‫א‬‫א‬‫א‬‫א‬١٠J ١٤ Power Triangle‫א‬ ١J ١٠J ١٤ ،‫א‬‫א‬ RL ‫א‬‫א‬ RL ‫א‬،   K‫א‬‫א‬‫א‬‫א‬‫א‬ RL ‫א‬‫א‬ I R  XL  Vs VR  VL     ‫א‬‫א‬RL‫א‬E٣٣J ١٤F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W I rms ‫א‬ VS rms θ VL rms  VS rms . I rms  Pa VS rms . I rms θ VR rms Ptrue  ‫א‬‫א‬E٣٤J ١٤F     W  K‫א‬‫א‬‫א‬‫א‬ VR C I rms rms  K‫א‬‫א‬ V Lrms C I rms  KApparent Power‫א‬‫א‬ VS C I rms rms  - ٣٤٤ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬،Power Triangle‫א‬  Pa  Pr θ  Ptrue   ‫א‬E٣٥J ١٤F   Powers Relationship‫א‬ ٢J ١٠J ١٤  WApparent Power‫א‬‫א‬  Pa = V Srms * I rms =          Pr = Pa . sin θ      Ptrue = Pa . cos θ  2 V Srms 2 = I rms *Z  Z     E٣٨J ١٤F  WTrue Power‫א‬‫א‬  E٣٩J ١٤F  E٤٠J ١٤F  WReactive Power‫א‬‫א‬    Power Units‫א‬‫א‬٣J ١٠J ١٤  (W )  Watt W‫א‬‫א‬  (VAR )  Volt − Ampere − Re active W‫א‬‫א‬  (VA)  Vott − Ampere W‫א‬‫א‬   - ٣٤٥ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    The Significance of apparent Power‫א‬‫א‬ ٤J ١٠J ١٤ ،EFApparent Power‫א‬‫א‬ ‫א‬  ‫א‬‫א‬K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ E‫א‬‫א‬F‫א‬‫א‬‫א‬ ‫א‬‫א‬K ‫א‬ ‫א‬‫א‬‫א‬،  K    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬، PF : thePowerFactor ‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    (PF) The Power Factor ‫א‬ ٥J ١٠J ١٤ ،‫א‬‫א‬‫א‬،Power Factor‫א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،PF‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬   PF = Ptrue = cos θ Pa PF = cos θ                  E٤١J ١٤F  W E٤٢J ٤>F    K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ W θ  ‫א‬،‫א‬‫א‬ θ ‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬    K‫א‬‫א‬ - ٣٤٦ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٨J ١٤F  W‫א‬،‫א‬‫א‬  I = 0.24 A  Ptrue = 20 w    ١ ‫ﺟﻬﺎز‬ Vs PF=0.75 110 v      I = 0.196 A  Ptrue = 20 w   Vs 110 v   ١ ‫ﺟﻬﺎز‬ PF=0.95     E٨J ٤>F‫א‬‫א‬‫א‬E٣٦J ١٤F  ‫א‬ 20w ‫א‬‫א‬‫א‬ 2,1‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬   ‫א‬K ‫א‬‫א‬    (PF = 0.75) ‫א‬‫א‬ ‫א‬‫א‬‫א‬، (PF = 0.95) ‫א‬‫א‬‫א‬  K‫א‬ - ٣٤٧ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Summary RL ‫א‬‫א‬‫א‬ RC ‫א‬‫א‬‫א‬  ‫א‬‫א‬ RC ‫א‬  ‫א‬‫א‬ RL ‫א‬   ‫א‬‫• א‬  Z = R2 + X L ⎛X ⎞ θ = tan ⎜ L ⎟ ⎝ R ⎠ ‫א‬‫• א‬ θ ‫א‬  2  Z = R2 + XC ⎛ XC ⎞ ⎟ ⎝ R ⎠ 2 ‫• א‬ θ = tan −1 ⎜ ‫א‬‫א‬ • ⎛V ⎞ θ = tan −1 ⎜⎜ L ⎟⎟ ⎝ VR ⎠ 2 2 2 VS = VR + VL θ ‫א‬  ‫• א‬ −1    • - ٣٤٨ - ‫א‬‫א‬ • ⎛V ⎞ θ = tan ⎜⎜ C ⎟⎟ ⎝ VR ⎠ 2 2 2 V S = V R + VC −1 •   ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   RL ‫א‬‫א‬‫א‬  RC ‫א‬‫א‬‫א‬  ‫א‬‫א‬ RC ‫א‬  ‫א‬‫א‬ RL ‫א‬   ‫א‬‫• א‬  Z= R. X L R2 + X L ⎛ R Q = tan −1 ⎜⎜ ⎝ XL ⎞ ⎟⎟ ⎠  θ ‫א‬   2  ‫• א‬  ‫א‬‫א‬ • ⎛I ⎞ Q = tan −1 ⎜⎜ L ⎟⎟ ⎝ IR ⎠ 2 2 2 IT = I R + I L •   Req = Z . cos θ  X Leq = Z . sin θ Leq = X Leq 2πF = Z= θ ‫א‬ RX C R2 + XC 2 ‫• א‬ ⎛ R ⎝ XC ⎞ ⎟⎟ ⎠ ‫א‬‫א‬ • −1 ⎛ I C ⎞ θ = tan ⎜⎜ ⎟⎟ ⎝ IR ⎠ 2 2 2 • IT = I R + IC θ = tan −1 ⎜⎜  W‫א‬‫א‬‫א‬‫א‬‫• א‬  W‫א‬‫א‬‫א‬‫א‬‫• א‬  ‫א‬‫• א‬ Z . sin θ 2πF Req = Z . cos θ X Ceq = Z . sin θ C eq = 1 1 = 2π .F . X Ceq 2π .F .Z . sin θ   - ٣٤٩ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬  1A ‫א‬‫א‬‫א‬‫א‬، 100mH  K١ W‫א‬‫א‬،B,A ‫א‬‫א‬ K٢ ١L A  1H L2 L3 10 H 5H   B L2= 50 mH A    L1 L3 100m H m H ٦٠     B  W‫א‬‫א‬‫א‬ K٣ ١L 50m H Vrms 10 v L2 L3 20m H 40m H    F= 2.5KHZ    K‫א‬‫א‬‫א‬‫א‬‫א‬ K K L3 , L2 ‫א‬‫א‬ K  - ٣٥٠ -  L4 40 H  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   R W‫א‬‫א‬‫א‬ K٤  XL  50 Ω  100 Ω Vs  10 v    R1  L1 L2  50mH 100mH  47 Ω Vs  10 v F= 100HZ   R  470 Ω  Vrms  10 v  F= 20KHZ L1 L2 5m H 8m H   Vrms  R1  10 v 560 Ω F= 20KHZ R2 330 Ω L1 L2 5m H 8m H      KImpedance‫א‬ - ٣٥١ -  ‫א‬‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    W‫א‬‫א‬‫א‬ K٥  I‫א‬‫א‬ K θ ‫א‬‫א‬ V L , V R  K  K  W‫א‬‫א‬‫א‬‫א‬‫א‬ RL ‫א‬‫א‬ K٦   I L , I R , I T ، W‫א‬‫א‬‫א‬ K٧  ‫א‬ K   IT ‫א‬‫א‬‫א‬‫א‬ K  I R2 , I L ‫א‬ K PF ‫א‬ Pa ‫א‬‫א‬ K Pr ‫א‬‫א‬ Ptrue ‫א‬‫א‬ - ٣٥٢ - K  ‫א‬‫א‬‫א‬ ‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ١٥  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ٪٩٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬    ٤ W‫א‬‫א‬‫א‬‫א‬      W‫א‬‫א‬  K -  K‫א‬‫א‬  ‫א‬‫א‬‫א‬ W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   - ٣٥٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Introduction١J ١٥ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬K  Series RLC Circuits ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K  Parallel RLC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  KResonance Circuits‫א‬   Series RLC Circuit RLC ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ١٥  RLC Circuits Characteristics‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١٥ W‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬RLC‫א‬E١J ١٥F  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬       ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢J ١٥F - ٣٥٤ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     K‫א‬ VR , I W  K 90 o ‫א‬‫א‬ VL  I WE‫א‬F‫א‬  K 90 o ‫א‬‫א‬ VC  I W‫א‬ 180 ‫א‬‫א‬‫א‬،E٢J ١٥F‫א‬ 0  K‫א‬‫א‬‫א‬ VC , V L ‫א‬‫א‬ Total Reactance‫א‬‫ א‬٢-٢-١٥ ،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  W‫א‬        ‫א‬‫א‬E٣J ١٥F  XT = Xl − XC    W E١J ١٥F  W‫א‬  ‫א‬‫א‬ ⇐ X L > X C  ‫א‬‫א‬ ⇐ X C  ‫א‬‫א‬‫א‬‫א‬ X C - ٣٥٥ - > XL = XL   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Total Impedance‫א‬‫ א‬٣-٢-١٥  W‫א‬‫א‬         ‫א‬‫א‬E٤J ١٥F   W‫א‬‫א‬‫א‬‫א‬‫א‬ Z T = R 2 + X T2 = R 2 + ( X L − X C ) 2    E٢J ١٥F Phase Angle‫א‬‫א‬ ٤-٢-١٥  W‫א‬‫א‬‫א‬‫א‬‫א‬ θ ‫א‬‫א‬  ⎛ XT ⎞ ⎟  ⎝ R ⎠ θ = tan −1 ⎜  E٣J ١٥F K θ ‫א‬‫א‬ ⇐ X L < X C ‫א‬‫א‬‫א‬،  K θ ‫א‬‫א‬ ⇐ X C < X L ‫א‬‫א‬‫א‬  E١J ١٥F  W‫א‬‫א‬‫א‬     E١J ١٥F‫א‬‫א‬‫א‬E٥J ١٥F    K‫א‬‫א‬‫א‬‫א‬  ‫א‬  1 = 3.18Ω 2πF .C X L = 2πF .L = 6.28Ω - ٣٥٦ XC =  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬ ⇐ X C < XL   W‫א‬‫א‬  X T = X L − X C = 3.1Ω  W‫א‬  2 Z T = R 2 + X T = 6 .4 Ω  W‫א‬‫א‬   ⎛ XT ⎞ 0 ⎟ = 29 ⎝ R ⎠ θ = tan −1 ⎜ 29 0 ‫א‬‫א‬‫א‬‫א‬ X C < X L        ‫א‬‫א‬‫א‬E٦J ١٥F  ‫א‬‫א‬ VLC ‫א‬E‫א‬F‫א‬، ‫א‬‫א‬‫א‬ VLC ‫א‬‫א‬،‫א‬‫א‬  K θ = 29 o ‫א‬ I  VS ، θ = 90 o           - ٣٥٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    Analysis of Series RLC Circuits‫א‬‫א‬‫א‬‫א‬٥J ٢J ١٥ ‫א‬‫א‬‫א‬‫א‬RLC‫א‬‫א‬E‫א‬F‫א‬  K‫א‬ V L , VC ‫א‬‫א‬‫א‬K180 0 ‫א‬‫א‬  E٢J ١٥F  W‫א‬‫א‬‫א‬             E٢J ١٥F‫א‬‫א‬‫א‬E٧J ١٥F  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K   K VLC ‫א‬‫א‬‫א‬ K  ‫א‬  W،‫א‬ K  Z = R 2 +( X L − X C )2 = 82.8Ω  W I= VS = 121mA Z V R = I .R = 9.08V VC = I . X C = 7.26V V L = I . X L = 3.03V - ٣٥٨ - W،‫א‬ K   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W، VL ‫א‬‫א‬‫א‬ K  C  V LC = VC − VL = 4.23V  K VC ‫א‬‫א‬‫א‬  W‫א‬‫א‬  ⎛ XT ⎞ ⎟ = 25 0 ⎝ R ⎠ θ = tan −1 ⎜  K 250 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ X L < X C ‫א‬   W         ‫א‬‫א‬‫א‬E٨J ١٥F    Series Resonance‫א‬‫א‬ ٦-٢-١٥ ‫א‬‫א‬EF‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬ X L > X C ‫א‬‫א‬‫א‬ X L < X C  X C ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  W‫א‬ X L ‫א‬‫א‬ - ٣٥٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬‫א‬‫א‬E٩J ١٥F 1 2πF .C    XC =  X L = 2πF .L   W E٤J ١٥F  E٥J ١٥F  W،‫א‬‫א‬‫א‬‫א‬‫א‬  ↑ X L , ↓ X C ⇐↑ F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، X C = X L ‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬،‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K Fr ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  W،‫א‬‫א‬،‫א‬‫א‬،E‫א‬F   X L = X C ⇒ V L = VC  Z r = R   - ٣٦٠ -   E٦J ١٥F E٧J ١٥F  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     W‫א‬        ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٠J ١٥F    Series Resonant Frequency Fr ‫א‬‫א‬ ٧-٢-١٥  X L = X C   ⇒ 2π .Fr .L =  ⇒ Fr =  ⇒ Fr = 2 1 2π .Fr .C 1 2π L.C E٨J ١٥F   E٩J ١٥F   E١٠J ١٥F   E١١J ١٥F (2π )2 .L.C 1   W،‫א‬  W‫א‬‫א‬‫א‬‫א‬  Fr = 1 2π L.C E١٢J ١٥F E٣J ١٥F - ٣٦١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    W‫א‬‫א‬‫א‬‫א‬             E٣J ١٥F‫א‬‫א‬‫א‬E١١J ١٥F  Fr = 1 2π LC  ‫א‬ = 318kHz ‫א‬‫א‬‫א‬‫א‬ X C = X L ،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬، 180 0 ‫א‬   ‫א‬‫א‬‫א‬E١٢J ١٥F   X T ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬  - ٣٦٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     E٤J ١٥F  W‫א‬ Z , X C            E٤J ١٥F‫א‬‫א‬‫א‬E١٣J ١٥F  X C = X L = 50Ω ‫א‬  Z = R = 100Ω ‫א‬  ‫א‬‫א‬‫א‬‫א‬٨J ٢J ١٥  Voltage, Current and Impedance Variation with Frequency  W Fr >F ‫א‬W F‫א‬‫א‬‫א‬‫א‬، F = 0 Hz ‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬E DC ، X C − X L ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫ א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  W،  F ↑⇒ X C ↓⇒ X L ↑⇒ ( X C − X L ) ↓⇒ Z ↓⇒ I ↑  W  ⇒ V R ↑⇒ V L ↑⇒ VC ↑  W  ⇒ V L − VC ↓ - ٣٦٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   ‫א‬‫א‬، X L    F = Fr ‫א‬W = X C ‫א‬‫א‬‫א‬‫א‬ KE‫א‬‫א‬F‫א‬‫א‬، VC = VL ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  W،‫א‬  F = Fr ⇒ X L = X C ⇒ VC = V L ⇒ VCL = 0  W  ⇒Z =R⇒I = VS ⇒ VS = VR R   W F > Fr ‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬،‫א‬ ،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  W  Fr ↑⇒ X L ↑⇒ X C ↓⇒ X L − X C ↑⇒ Z ↑⇒ I ↓⇒ V R ↓, VC ↓, V L ↓⇒ V L − VC ↑   VR ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬، VS ‫א‬‫א‬ VC ‫א‬      - ٣٦٤ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬        ‫א‬RLC‫א‬‫א‬‫א‬‫א‬‫א‬E١٤J ١٥F   Phase Angle Variation with Frequency‫א‬‫א‬‫א‬ ٩-٢-١٥ ‫א‬‫א‬‫א‬‫א‬‫א‬  Fr > F ⇒ X C > X L    W،‫א‬ E١٣J ١٥F ‫א‬‫א‬،‫א‬‫א‬‫א‬‫ א‬  W، F = Fr ‫א‬  - ٣٦٥ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      ‫א‬‫א‬‫א‬E١٥J ١٥F ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬، θ = 0 0 ‫א‬‫א‬، ،‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  W‫א‬   F = Fr  F⟩ Fr   ‫א‬‫א‬‫א‬E١٦J ١٥F  W XT = ، X T  X L .X C XL − XC  E١٤J ١٥F   = ∞ ،‫א‬‫א‬ ⇐ X L = X C   W‫א‬  ‫א‬‫א‬E١٧J ١٥F - ٣٦٦ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     Parallel RLC Circuit RLC ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٥  RLC Circuits Characteristics‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٣J ١٥  W‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬       ‫א‬‫א‬RLC‫א‬E١٨J ١٥F  W  VR = VC = VL = VS  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬ VR , I R W  K 90 o ‫א‬‫א‬ VL  I L WE‫א‬F‫א‬  K 90 o ‫א‬‫א‬ VC  I C W‫א‬        ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٩J ١٥F  I C , I L ‫א‬‫א‬ ⇐ 180 0 ‫א‬‫א‬‫א‬،‫א‬  WK‫א‬‫א‬‫א‬ - ٣٦٧ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    I LC = I L − I C    E١٥J ١٥F Total Reactance‫א‬‫ א‬٢-٣ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W  X L .X C 1 1 1 = − ⇒ XT = XT XL XC XL − XC   E١٦J ١٥F  Total Impedance‫א‬‫ א‬٣-٣-١٥ ‫א‬‫א‬،‫א‬‫א‬ RLC ‫א‬‫א‬‫א‬  W‫א‬  ZT = R. X T R + XT 2 2   E١٧J ١٥F Phase Angle‫א‬‫א‬ ٤-٣-١٥  W، θ ‫א‬‫א‬  ⎛ R ⎝ XT θ = tan −1 ⎜⎜ ⎞ ⎟⎟   ⎠  E١٨J ١٥F  E٥J ١٥F  W‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬        E٥J ١٥F‫א‬‫א‬‫א‬E٢٠J ١٥F  - ٣٦٨ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    XT = ZT =  X L .X C 5 * 10 = = 10Ω XL − XC 5 R. X T R 2 + X T2 = 10 * 10 10 2 + 10 2 = 7.07Ω  W،‫א‬‫א‬  ⎛ R ⎝ XT θ = tan −1 ⎜⎜ ⎞ ⎟⎟ = 45 o  ⎠ Parallel Resonance‫א‬‫א‬ ٥-٣-١٥  W،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  XL = XC ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬، 180 0 ‫א‬  W‫א‬‫א‬‫א‬K I LC  = 0 A ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬E٢١J ١٥F ،K‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ I LC = 0 ‫א‬‫א‬ ‫א‬‫א‬‫א‬،Open Circuits‫א‬  W‫א‬،‫א‬‫א‬‫א‬K‫א‬  XT = XLXC XL − XC   E١٩J ١٥F  - ٣٦٩ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   ‫א‬‫א‬،، X T  = ∞ ‫א‬ X L = X C    W،‫א‬      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٢J ١٥F ، θ = 0 o ،‫א‬‫א‬‫א‬، X L = X C W‫א‬‫א‬  K‫א‬‫א‬  The Parallel Resonant Frequency‫א‬‫א‬٦J ٣J ١٥  W‫א‬‫א‬‫א‬، Fr ‫א‬‫א‬‫א‬  Fr = 1 2n LC   E٢٠J ١٥F  W‫א‬‫א‬ 1 1 W F < Fr W‫א‬‫א‬ < XC XL K‫א‬‫א‬ ⇐ 1 = 1 W F = Fr W‫א‬‫א‬ XC XL  K‫א‬‫א‬ ⇐ 1 < 1  F > Fr W‫א‬‫א‬ XL XC  K‫א‬‫א‬ ⇐  ⎧   ⎨ 1 1 > ⎩XL XC  1 1 ⎫ > ⎬  XC XL ⎭  ‫א‬RLC‫א‬‫א‬E٢٣J ١٥F - ٣٧٠ - K١ K٢ K٣  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬   1 2πF .C   W    XC =  X L = 2πF .L  E٢١J ١٥F  E٢٢J ١٥F  E٦J ١٥F  W‫א‬‫א‬‫א‬       E٦J ١٥F‫א‬‫א‬‫א‬E٢٤J ١٥F   K‫א‬‫א‬‫א‬،‫א‬،‫א‬  Fr = 1 2π LC  ‫א‬ = 2.25kHz  W‫א‬‫א‬  Fr = 2.25 Hz  ‫א‬‫א‬    XT = ∞  ‫א‬ Z = R = 100Ω  ‫א‬‫א‬ IT = VS = 0 .1 A R   - ٣٧١ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬     ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ K١        R = 10Ω ، L = 5mH ، C = 0.05µF ، F = 5kH 2 W  W‫א‬‫א‬‫א‬ K٢            (P r  (P 2 true 2 = I rms * R = I rms * X T (P a  ) P I T ‫א‬‫א‬ true  K ‫א‬‫א‬ K  )  P ‫א‬‫א‬ K = VS rms .I rms r )  P ‫א‬‫א‬‫ א‬K  a  R2 ‫א‬‫א‬ R1 ‫א‬‫א‬ K - ٣٧٢ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬    ‫א‬ L2 ‫א‬‫א‬ L1 ‫א‬‫א‬ R2  R1 ‫א‬‫א‬ K  C 2 ,C1 ‫א‬  E‫א‬‫א‬‫א‬F θ ‫א‬‫א‬ K   W‫א‬‫א‬‫א‬K K٣        K‫א‬ •  K‫א‬‫א‬ I ‫א‬ Z , X C , X L  •   W‫א‬‫א‬‫א‬ K٤            - ٣٧٣ -  ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬      K Z T ‫א‬‫א‬ K ‫א؟‬‫؟‬‫א‬‫א‬ K    K I LC ‫א‬‫א‬‫א‬‫א‬ I C , I L , I R ‫א‬ K  - ٣٧٤ -   ‫א‬‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬    EReferencesF‫א‬‫א‬  [1] Thomas L. Floyed, Electrical Engineering Fundamentals, Prentice, Inc, sixth edition, 2000. [2] B. L. Theraja, A. K. Theraja, " Electrical Technology", published by Ninja Construction development Co. Ltd. Ram Nagar, New Delhi, 110055, 1995. [3] M. A. PAI, "Introduction to Electric Circuits and Machines", Affiliated east west presses private limited, 1975. - ٣٥٣ -  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬     ‫א‬  K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K   K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K   ١K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Introduction١J ١  ٢K K K K K K K K K K K K K K K K K K K The International System of Units‫א‬‫א‬‫א‬1-2  ٢K K K K K K K K K K K K K K K K K K K K K K K K The Measurement Units‫א‬‫א‬1-2-1  ٣ K K K K K K K K K K K K K K K K K K K K K K K K K Electric Quantities‫א‬‫א‬1-2-2  ٤K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٥K K K K K K K K K K K K K K K K K K K K K K K K Scientific Notation‫א‬‫א‬1-3 ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١  ٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬1-5  ٧K K K K K K K K K K K K K K K K K K K K Measurement units Conversion‫א‬‫א‬1-6  ٩ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬  ١١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬W‫א‬‫א‬  ١٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Introduction١J ٢  ١٢ K K K K K K K K K K K K K K K K K K K K K K K K K K Electrical Charge‫א‬‫א‬٢J ٢  ١٣ K K K K K K K K K K K K K K K K K K K K K K K K K K Electrical Voltage‫א‬‫א‬٣J ٢  ١٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Voltage‫א‬١J ٣J ٢  ١٤ K K K K K K K K K K K K K K K K K K K K K K K K K K K Voltage Sources‫א‬2-3-2  ١٥ K K K K K K K K K K K K K K K K K K K K K K K K K K Electrical Current‫א‬‫א‬٤J ٢  ١٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Current‫א‬١J ٤J ٢  ١٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K Current Types‫א‬‫א‬٢J ٤J ٢  ١٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Resistance‫א‬٥J ٢  ١٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K Resistor‫א‬١J ٥J ٢  ١٩ K K K K K K K K K K K K K K K K K K K K K K Resistance of a wire‫א‬‫א‬٢J ٥J ٢  ٢٠ K K K K K K K K K K K K K K K K K K K K K K K K Types of Resistors‫א‬‫א‬٣J ٥J ٢  ٢٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K Conductance‫א‬٤J ٥J ٢ Energy and Power‫א‬‫א‬6-2  ٢٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٣ K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬١J ٦J ٢ Units of Energy‫א‬‫א‬٢J ٦J ٢  ٢٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ W‫א‬‫א‬ Introduction١J ٣  ٢٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Ohm’s Law٢J ٣  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬    ٢٨ K K K K K K K K K K K K K K K K K K K K K K K K  Current Formula‫א‬EF2-3-1  ٣٠ K K K K K K K K K K K K K K K K K K K K K K K K K Resistance Formula‫א‬2-3-1  ٣١ K K K K K K K K K K K K K K K K K K K K K K K K K K Voltage Formula2-3-1  ٣٢ K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٢ K K K K K K K K K K K K K K K K K K K K K K K K K Voltage Drop‫א‬3-2-3-1 Voltage Source‫א‬3-2-3-2  ٣٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٤٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬ ‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬  ٤٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Introduction4-1  ٤٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٤٦ K K K K K K K K K K K K K K K K K K K K Summary‫א‬ Power‫א‬4-2 Power in Electric Circuit‫א‬‫א‬‫א‬‫א‬4-3  ٥٠ K K K K K K K K K K K K K K K K K K K K K Power Rating of Resistors‫א‬‫א‬4-4  ٥٠ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Definition١J ٤J ٤  ٥٠ K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٤J ٤  ٥١ K K K K K K K K K K K K K K K K K K K K K K Resistor Failures‫א‬EF٣J ٤J ٤  ٥٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٥٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٥٤ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Introduction5-1 Series Connection‫א‬‫א‬‫א‬5-2  ٥٦ K K K K K K K K K K K K K K K K K K K K K K K K  ٥٧ K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬W‫א‬‫א‬  ٥٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٥٥ K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ Total Resistance (RT)‫א‬‫א‬5-2-1 Ohm's Law in Series Circuits‫א‬‫א‬‫א‬5-3  ٦٠ K K K K K K K K K K K K K K K K K K K K K  ٦٢ K K K K K K K K K K K K K K K K K K K K Voltage Sources in Series‫א‬‫א‬‫א‬5-4 E Kirchhoff's voltage law (KVL5-5  ٦٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Voltage Divider‫א‬5-6  ٦٥ K K K K K K K K K K K K K K K K K K K K K K Voltage Divider Law‫א‬١J ٦J ٥  ٧٢ K K K K K K K K K K K K K K K K K K K K K K  ٧٦ K K K K K K K K K K K K K K K K K Power in a Series Circuit‫א‬‫א‬‫א‬‫א‬5-7 Voltage With Respect to Ground‫א‬5-8  ٧٩ K K K K K K K K K K K K K K K K K K K K K K K K K K K Troubleshooting‫א‬‫א‬5-9  ٨٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٨٤ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٩١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٩٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٩٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬W‫א‬‫א‬ Introduction١J ٦ Parallel Circuit‫א‬‫א‬‫א‬٢J ٦  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬    ٩٣ K K K K K K K K K K K K K K K K K K K K K K K K  ٩٥ K K K K K K K K K K K K K K  Total Resistance (RT)‫א‬5-2-2 Voltage Drop in Parallel Circuit‫א‬‫א‬‫א‬‫א‬‫א‬٣J ٦  ٩٥ K K K K K K K K K K K K K K K K K K K K K K Kirchhoff’s Current Law٤J ٦  ٩٩ K K K K K K K K K K K K K K Total Parallel Resistors‫א‬‫א‬‫א‬‫א‬‫א‬٥J ٦  ٩٩ K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬١J ٥J ٦  ١٠٢ K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬٢J ٥J ٦  ١٠٣ K K K K K K K K K K Determining an unknown Parallel Resistor‫א‬‫א‬‫א‬٧J ٦  ١٠٦ K K K K K K K K K K K K Current Division in Parallel Circuits‫א‬‫א‬‫א‬‫א‬EF٦J ٦  ١١٣ K K K K K K K K K K K K K K K K K K K K K Power in Parallel Circuits‫א‬‫א‬‫א‬‫א‬٧J ٦  ١١٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١١٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١١٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ ‫א‬‫א‬ E‫א‬-‫א‬F‫א‬W‫א‬‫א‬  ١١٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Introduction١J ٧  ١١٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬–‫א‬‫א‬‫א‬٢J ٧  ١٢٤ K K K K K K K K K K K K K K K Analysis of Series-Parallel Circuits‫א‬‫א‬–‫א‬‫א‬‫א‬٣J ٧  ١٤١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٧  ١٤٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٤٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٥٠ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬ ‫א‬‫א‬‫א‬W‫א‬‫א‬  ١٥١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٥١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ Introduction8-1 ‫א‬‫א‬‫א‬‫א‬8-2  ١٥١ K K K K K K K K K K K K K K K K K K K K Constant Voltage Source‫א‬‫א‬8-2-1  ١٥٢ K K K K K K K K K K K K K K K K K K K K K Constant Current Source٢J ٢J ٨  ١٥٣ K K K K K K K K K K K K K K K K K K K K K K K K Source Conversions‫א‬8-2-3  ١٥٦ K K K K K K K K K K K K K K K K K K K K K K K K K Superposition Theorem‫א‬8-3  ١٥٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬8-3-1  ١٥٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٥٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٦٧ K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٧٥ K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٧٩ K K K K K K K K K K K K K K K K K K K K  ١٨٤ K K K K K K K K K K K K K K K K ‫א‬‫א‬8-3-2 ‫א‬٣J ٣J ٨ Thevenin's Theorem٤J ٨ ‫א‬‫א‬8-4-1 Maximum Power Transfer‫א‬‫א‬8-4-2 E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬8-5  ١٩١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ١٩٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K 'Summary'‫א‬ ‫א‬‫א‬  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬     ١٩٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ١٩٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Introduction١J ٩  ١٩٦ K K K K K K K K K K K K K K K K K K K K K K K K Capacitor Characteristics‫א‬‫א‬٢J ٩  ١٩٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K Basic Structure‫א‬١J ٢J ٩  ١٩٦ K K K K K K K K K K K K K K K How Capacitors Store charges‫א‬٢J ٢J ٩  ١٩٩ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٠٠ K K K K K K K K K K K K K K K K K K K K K Capacitance‫א‬٣J ٢J ٩ Voltage Rating‫א‬‫א‬‫א‬‫א‬٤J ٢J ٩  ٢٠٠ K K K K K K K K K K K K K K K K K K K K K K Temperature Coefficient‫א‬‫א‬‫א‬٥J ٢J ٩ Dielectric Strength‫א‬٦J ٢J ٩  ٢٠١ K K K K K K K K K K K K K K K K K K K K K K K K  ٢٠١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٠٢ K K K K K K K K K K K K Leakage‫א‬٧J ٢J ٩ Physical Characteristics of Capacitors‫א‬‫א‬‫א‬٨J ٢J ٩ Types of Capacitors‫א‬‫א‬٣J ٩  ٢٠٤ K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٠٤ K K K K K K K K K K K K K K K K K K K K K K K K Variable Capacitors‫א‬‫א‬٢J ٣J ٩  ٢٠٦ K K K K K K K K K K K K K K K K K K K K K K K  ٢٠٧ K K K K K K K K K K K K K K K K K K Fixed Capacitors‫א‬‫א‬١J ٣J ٩ Connection Types of Capacitors‫א‬‫א‬٤J ٩  ٢٠٧ K K K K K K K K K K K K K K K K K K K K K K K K Series Capacitors‫א‬‫א‬١J ٤J ٩  ٢٠٨ K K K K K K K K K K K K K K K K K K K K K K K K Parallel Capacitors‫א‬‫א‬٢J ٤J ٩  ٢١٠ K K K K K K K K K K K K K K K K Charging & Discharging of Capacitors‫א‬٥J ٩  ٢١٠ K K K K K K K K K K K K K K K K K K K K K K K K Charging Capacitors‫א‬١J ٥J ٩  ٢١١ K K K K K K K K K K K K K K K K K K K K K K Discharging Capacitors‫א‬٢J ٥J ٩  ٢١٢ K K K K K K K K K K K K K K K K K K K K K K K K K  ٢١٢ K K K K K K K K K K K K K K RC Time Constant‫א‬٣J ٥J ٩ Charging and Discharging Curves‫א‬‫א‬٤J ٥J ٩  ٢١٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢١٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ٢١٩ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢١٩ K K K K K K K K K K K K K K K K K K K K K Introduction١J ١٠ Inductance CharacteristicsE‫א‬F‫א‬‫א‬٢J ١٠  ٢١٩ K K K K K K K K K K K K K K K K K K K K K K K K K K K Basic Structure‫א‬١J ٢J ١٠  ٢٢٠ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٢٠ K K K K K K K K K K K K K K K ‫א‬‫א‬ Inductance‫א‬٢J ٢J ١٠ How Inductors Store charges‫א‬٣J ٢J ١٠  ٢٢١ K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٢J ١٠  ٢٢١ K K K K K K K K K K K K K K K K K K K K K K  ٢٢١ K K K K K K K K K K K K K K K K K K K K K K K  ٢٢٢ K K K K K K K K K K K K K K PermeabilityE‫א‬F‫א‬١J ٤J ٢J ١٠ ‫א‬‫א‬‫א‬٢J ٤J ٢J ١٠ Winding Resistance and Capacitance‫א‬‫א‬٥J ٢J ١٠  ٢٢٣ K K K K K K K K K K K K K K K K K K K K K K K K K Inductors TypesE‫א‬F‫א‬‫א‬٣J ١٠  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬    ٢٢٤ K K K K K K K K K K K K K K K K K K K Connection Types of Inductors‫א‬‫א‬٤J ١٠ Series Inductors‫א‬‫א‬‫א‬١J ٤J ١٠  ٢٢٤ K K K K K K K K K K K K K K K K K K K K K K K Parallel Inductors‫א‬‫א‬‫א‬٢J ٤J ١٠  ٢٢٤ K K K K K K K K K K K K K K K K K K K K K K  ٢٢٥ K K K K K K K K K K K K K K K K K K K  Inductors in DC Circuits‫א‬‫א‬‫א‬‫א‬٥J ١٠  ٢٢٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬  ٢٢٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٣٠ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬W‫א‬‫א‬  ٢٣١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٣١ K K K K K K K K K K K K  ٢٣١ K K K K K K K ‫א‬‫א‬ Introduction١J ١١ Magnetic Effects of Electrical Current‫א‬‫א‬‫א‬٢J ١١ Generation & Concentration of Magnetic Field‫א‬‫א‬١J ٢J ١١  ٢٣٣ K K K K K K K K K K K K K K Basic Concepts of Electrical Generator‫א‬‫א‬٣J ١١  ٢٣٤ K K K K K K K K K K K K K K K K K K K  ٢٣٥ K K K K K K K K K K K K K K K K  ٢٣٦ K K K K K K K K K K K K K K  ٢٣٧ K K K K K K K K K K K Generation of Sine Wave‫א‬‫א‬١J ٣J ١١ Evaluation of Sine Wave‫א‬‫א‬‫א‬٢J ٣J ١١ Representation of Sine Wave‫א‬‫א‬‫א‬٣J ٣J ١١ Mathematical Representation of Vectors‫א‬‫א‬٤J ٣J ١١  ٢٣٨ K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬‫א‬EACF‫א‬‫א‬٤J ١١  ٢٣٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٤٠ K K K K K K K K K K K K K K K K K K K K K K  ٢٤١ K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬١J ٤J ١١ ‫א‬‫א‬‫א‬‫א‬٢J ٤J ١١ Sine wave Voltage SourcesE‫א‬F‫א‬‫א‬٣J ٤J ١١  ٢٤١ K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬EACF‫א‬‫א‬‫א‬٥J ١١  ٢٤١ K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬١J ٥J ١١  ٢٤٢ K K K K K K K K K K K K K K K K K K K K K K K Instantaneous Value‫א‬‫א‬٢J ٥J ١١  ٢٤٢ K K K K K K K K K K K K K K K K K K K K K K K Peak ValueE‫א‬‫א‬F٣J ٥J ١١  ٢٤٣ K K K K K K K K K K K K K K K K K K K K K Peak to Peak Value‫א‬‫א‬‫א‬٤J ٥J ١١  ٢٤٣ K K K K K K K K K K K K K K K Effective value of sine wave‫א‬‫א‬‫א‬٥J ٥J ١١  ٢٤٤ K K K K K K K K K K K K K K K Average value of sine wave‫א‬‫א‬‫א‬٦J ٥J ١١  ٢٤٥ K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬٦J ١١  ٢٤٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ١J ٦J ١١  ٢٤٦ K K K K K K K K K K K K K K K K Ohm's Law in AC Circuits‫א‬‫א‬‫א‬٢J ٦J ١١  ٢٤٧ K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬٣J ٦J ١١  ٢٤٨ K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬١J ٣J ٦J ١١  ٢٤٨ K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬٢J ٣J ٦J ١١  ٢٥١ K K K K K K K K K K K K K K K K K K K K K E‫א‬F٧J ١١  ٢٥١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ١J ٧J ١١  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬     ٢٥١ K K K K K K K K K K K K K K K K K K V DC > VP ‫א‬‫א‬‫א‬‫א‬٢J ٧J ١١  ٢٥٢ K K K K K K K K K K K K K K K K K K V DC < V P ‫א‬‫א‬‫א‬‫א‬٣J ٧J ١١  ٢٥٤ K K K K K K K K K K K K K K K K K K K K Non Sinusoidal Wave Forms‫א‬‫א‬٨J ١١  ٢٥٤ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٥٤ K K K K K K K K K K K K K K K ١J ٨J ١١ Repetitive Pulse Wave FormE‫א‬F٢J ٨J ١١  ٢٥٧ K K K K K K K K K K K K K K K K K K K K K K K K K K Square Wave‫א‬‫א‬٣J ٨J ١١  ٢٥٨ K K K K K K K K K K K K K K K K K K K K K K K Triangular Wave Form‫א‬‫א‬٤J ٨J ١١  ٢٥٩ K K K K K K K K K K K K K K K K K K K K K K Saw tooth Wave Form‫א‬٥J ٨J ١١  ٢٦٠ K K K K K K K K K K K K K K K K K K K K K K K K K K K K Harmonics‫א‬‫א‬٦J ٨J ١١  ٢٦٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٦٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٦٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٦٧ K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬ ‫א‬‫א‬W‫א‬‫א‬  ٢٦٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٦٦ K K K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ Introduction١J ١٢ Mutual Inductance‫א‬‫א‬٢J ١٢ The Basic Transformer‫א‬‫א‬٣J ١٢  ٢٦٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Structure١J ٣J ١٢  ٢٦٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬٢J ٣J ١٢  ٢٦٩ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ٣J ٣J ١٢  ٢٦٩ K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٧١ K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٧٣ K K K K K K K K K K K Turns Ratio‫א‬‫א‬٤J ١٢ Direction of Winding‫א‬‫א‬٤J ١٢ Inductance Voltage and Current Relationship‫א‬‫א‬‫א‬٥J ١٢  ٢٧٣ K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٥J ١٢  ٢٧٣ K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥J ١٢  ٢٧٤ K K K K K K K K K K K K K K K K K K K K K K K K K K Transformer Types‫א‬‫א‬٦J ١٢  ٢٧٤ K K K K K K K K K K K K K K K K K K K K K K K K Step–up Transformer١J ٦J ١٢  ٢٧٤ K K K K K K K K K K K K K K K K K K K K K K  ٢٧٦ K K K K K K K K K K K K K K K K K K Step–down Transformer٢J ٦J ١٢ Transformer Current Direction‫א‬‫א‬‫א‬٧J ١٢  ٢٧٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٧٩ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ ‫א‬‫א‬  ٢٨١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬W‫א‬‫א‬  ٢٨٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٨٢ K K K K K K K K K K K K K K K K K K K K K K Introduction١J ١٣ Capacitive Reactance X C ‫א‬‫א‬٢J ١٣  ٢٨٤ K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬٣J ١٣  ٢٨٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬٤J ١٣  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬     ٢٨٧ K K K K K K K K K K K K K K K K K K K K Power in Capacitor Circuits‫א‬‫א‬‫א‬٥J ١٣ Instantaneous Power‫א‬‫א‬١J ٥J ١٣  ٢٨٧ K K K K K K K K K K K K K K K K K K K K K K K  ٢٨٨ K K K K K K K K K K K K K K K K K K K K K K K K  ٢٨٨ K K K K K K K K K K K K K K K K K K K K K K K  ٢٨٩ K K K K K K K K K K K K True Power Ptrve ‫א‬‫א‬٢J ٥J ١٣ Pr Reactive Power‫א‬‫א‬٣J ٥J ١٣ Series & Parallel Capacitive AC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٦J ١٣  ٢٨٩ K K K K K K K K K K K K K K K K K K K K K K Series Capacitors‫א‬‫א‬‫א‬١J ٦J ١٣  ٢٩٠ K K K K K K K K K K K K K K K K K K K K K K Parallel Capacitors‫א‬‫א‬‫א‬٢J ٦J ١٣  ٢٩١ K K K K K K K K K K K K K K K K K K K K Series RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١٣  ٢٩١ K K K K K K K K K K K K Characteristics of RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٧J ١٣  ٢٩٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٩٢ K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٩٣ K K K K K K K K K K K K K Impedance Z‫א‬٢J ٧J ١٣ θ Phase Angle‫א‬‫א‬٣J ٧J ١٣ Voltages Relationships‫א‬‫א‬RC‫א‬‫א‬‫א‬٤J ٧J ١٣  ٢٩٤ K K K K K K K K K K K K K K K K K K K K Ohm's Law‫א‬‫א‬‫א‬‫א‬٥J ٧J ١٣  ٢٩٥ K K K K K K K K K K K Frequency Effect on RC ‫א‬‫א‬‫א‬‫א‬٦J ٧J ١٣  ٢٩٦ K K K K K K K K K K K K K K K K K K K K Parallel RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١٣  ٢٩٦ K K K K K K K K K K K K Characteristics of RC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ١٣  ٢٩٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٩٨ K K K K K K K K K K K K K K K K K K K K K K K K K K  ٢٩٩ K K K K K K K K K K K K K Impedance Z‫א‬٢J ٨J ١٣ Phase Angle θ ‫א‬‫א‬٣J ٨J ١٣ Currents Relationships‫א‬‫א‬RC‫א‬‫א‬‫א‬‫א‬٤J ٨J ١٣  ٣٠٠ K K K K K K K K K K K K K K K K K K K K Ohm's Law‫א‬‫א‬‫א‬‫א‬٥J ٨J ١٣  ٣٠٠ K K K K K K K K K K K K K K K K K K K K K K ‫א‬ RC ‫א‬ RC ‫א‬‫א‬٦J ٨J ١٣  ٣٠٣ K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬Summary  ٣٠٤ K K K K K K K K K K Series-Parallel RC Circuits‫א‬‫א‬‫א‬E‫א‬J ‫א‬F‫א‬‫א‬٩J ١٣  ٣٠٧ K K K K K K K K K K K K K K K K K K K K Power in RC Circuits‫א‬‫א‬‫א‬‫א‬١٠J ١٣  ٣٠٧ K K K K K K K K K K K K K K K K K K K K K K K K K K Power Triangle‫א‬١J ١٠J ١٣  ٣٠٨ K K K K K K K K K K K K K K K K K K K K K K K Powers Relationship‫א‬٢J ١٠J ١٣  ٣٠٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٠٨ K K K K K K K K K K K K K K ‫א‬‫א‬٣J ١٠J ١٣ The Significance of apparent Power‫א‬‫א‬٤J ١٠J ١٣  ٣٠٩ K K K K K K K K K K K K K K K K K K K K K K EThe Power Factor (PF‫א‬٥J ١٠J ١٣  ٣١١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣١٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣١٧ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬ ‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬  ٣١٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣١٨ K K K K K K K K K K K K K K K K K K K K K K K Summary‫א‬ Introduction١J ١٤ Inductive Reactance X L ‫א‬‫א‬٢J ١٤  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬    ٣٢٠ K K K K K K K K  Ohm's Law in Inductive AC Circuits‫א‬‫א‬‫א‬‫א‬٣J ١٤  ٣٢٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K Power in an Inductor‫א‬‫א‬‫א‬٥J ١٤  ٣٢٣ K K K K K K K K K K K K K K K K K K K K K K K  ٣٢٣ K K K K K K K K K K K K K K K K K K K K K K K Instantaneous Power‫א‬‫א‬١J ٥J ١٣  ٣٢٤ K K K K K K K K K K K K K K K K K K K K K K K K  ٣٢٤ K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬٤J ١٤ True Power Ptrue ‫א‬‫א‬٢J ٥J ١٤ Pr Reactive Power‫א‬‫א‬٣J ٥J ١٤ Series & Parallel Inductive AC Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٦J ١٤  ٣٢٦ K K K K K K K K K K K K K  ٣٢٦ K K K K K K K K K K K K K K K K K K K K K K K Series Inductors‫א‬‫א‬‫א‬١J ٦J ١٤  ٣٢٦ K K K K K K K K K K K K K K K K K K K K K K K Parallel Inductors‫א‬‫א‬‫א‬٢J ٦J ١٤  ٣٢٨ K K K K K K K K K K K K K K K K K K K K K WSummary‫א‬‫א‬‫א‬‫א‬‫א‬  ٣٣٠ K K K K K K K K K K K K K K K K K K K K K Series RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١٤  ٣٣٠ K K K K K K K K K K K K Characteristics of RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٧J ١٤  ٣٣١ K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٣٢ K K K K K K K K K K K K K K K K K K K K K K K K K K Impedance Z‫א‬٢J ٧J ١٤ θ Phase Angle‫א‬‫א‬٣J ٧J ١٤  ٣٣٢ K K K K K K K K K K K K K K Voltages Relationships‫א‬‫א‬RL‫א‬‫א‬‫א‬٤J ٧J ١٤  ٣٣٣ K K K K K K K K K K K K K K K K K K K K Ohm's Law‫א‬‫א‬‫א‬‫א‬٥J ٧J ١٤  ٣٣٤ K K K K K K K K K K K K Frequency Effect on RL ‫א‬‫א‬‫א‬‫א‬٦J ٧J ١٤  ٣٣٦ K K K K K K K K K K K K K K K K K K K K  ٣٣٦ K K K K K K K K K K K K Parallel RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١٤ Characteristics of RL Circuits‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ١٤  ٣٣٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٣٨ K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٣٩ K K K K K K K K K K K K K θ Phase Angle‫א‬‫א‬٣J ٨J ١٤ Currents Relationships‫א‬‫א‬RL‫א‬‫א‬‫א‬‫א‬٤J ٨J ١٤  ٣٣٩ K K K K K K K K K K K K K K K K K K K K Ohm's Law‫א‬‫א‬‫א‬‫א‬٥J ٨J ١٤  ٣٤٠ K K K K K K K K K K K K K K K K K K K K K K K  ٣٤٢ K K K K K K K K K K Impedance Z‫א‬٢J ٨J ١٤ ‫א‬ RL ‫א‬ RL ‫א‬‫א‬٦J ٨J ١٤ Series -Parallel RL Circuits‫א‬‫א‬‫א‬E‫א‬J ‫א‬F‫א‬‫א‬٩J ١٤  ٣٤٤ K K K K K K K K K K K K K K K K K K K K Power in RL Circuits‫א‬‫א‬‫א‬‫א‬١٠J ١٤  ٣٤٤ K K K K K K K K K K K K K K K K K K K K K K K K K K Power Triangle‫א‬١J ١٠J ١٤  ٣٤٥ K K K K K K K K K K K K K K K K K K K K K K K Powers Relationship‫א‬٢J ١٠J ١٤  ٣٤٥ K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٤٦ K K K K K K K K K K K K K K Power Units‫א‬‫א‬٣J ١٠J ١٤ The Significance of apparent Power‫א‬‫א‬٤J ١٠J ١٤  ٣٤٦ K K K K K K K K K K K K K K K K K K K K K K  ٣٤٨ K K K K K K K K K K K K K K K K K K EPFFThe Power Factor ‫א‬٥J ١٠J ١٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Summary  ٣٥٠ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٥٣ K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬  ١١١  ‫א‬  ‫א‬  ‫א‬     ٣٥٤ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Series RLC Circuit RLC ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ١٥  ٣٥٤ K K K K K K K K K K K K K K K K  ٣٥٤ K K K K K K K K K K Introduction١J ١٥ RLC Circuits Characteristics‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١٥  ٣٥٥ K K K K K K K K K K K K K K K K K K K K K K K K Total Reactance‫א‬‫א‬٢J ٢J ١٥  ٣٥٦ K K K K K K K K K K K K K K K K K K K K K K K Total Impedance‫א‬‫א‬٣J ٢J ١٥  ٣٥٦ K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٥٨ K K K K K K K K K K K K Phase Angle‫א‬‫א‬٤J ٢J ١٥ Analysis of Series RLC Circuits‫א‬‫א‬‫א‬‫א‬٥J ٢J ١٥  ٣٥٩ K K K K K K K K K K K K K K K K K K K K K K K K K Series Resonance‫א‬‫א‬٦J ٢J ١٥  ٣٦٣ K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬‫א‬‫א‬٨J ٢J ١٥  ٣٦٥ K K K K K K K K K K K K Phase Angle Variation with Frequency‫א‬‫א‬‫א‬٩J ٢J ١٥  ٣٦٧ K K K K K K K K K K K K K K K  ٣٦٧ K K K K K K K K K K Parallel RLC Circuit RLC ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٥ RLC Circuits Characteristics‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٣J ١٥  ٣٦٨ K K K K K K K K K K K K K K K K K K K K K K K Total Impedance‫א‬‫א‬٣J ٣J ١٥  ٣٦٨ K K K K K K K K K K K K K K K K K K K K K K K K K K K  ٣٦٩ K K K K K K K K K K K K K K K K K K K K K K K K  ٣٧٠ K K K K K K K K K K K K K K K K K Phase Angle‫א‬‫א‬٤J ٣J ١٥ Parallel Resonance‫א‬‫א‬٥J ٣J ١٥ The Parallel Resonant Frequency‫א‬‫א‬٦J ٣J ١٥  ٣٧٢ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K ‫א‬‫א‬  ٣٥٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K EReferencesF‫א‬‫א‬              ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬ GOTEVOT appreciates the financial support provided by BAE SYSTEMS 

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