‫جمهورية الع اة‬
‫أسم انجامؼت‪ :‬انجامؼت انتكىهُجيً‬
‫أسم انكهيت‪:‬قسم ٌىذست انهيزر َاالنكترَوياث انبصريت‬
‫أسم انقسم‪ :‬فرع ٌىذست االنكترَوياث انبصريت‬
‫أسم انمحاضر‪ :‬صالح انذيه ػذوان طً‬
‫انهقب انؼهمي‪ :‬مذرس‬
‫انمؤٌم انؼهمي‪ :‬دكتُراي‬
‫مكان انؼمم‪ :‬انجامؼت انتكىهُجيً‬
‫وز ورة اللعلية العالةوة البحة العجل ة‬
‫معز ة إلشع فة القهرية العجل‬
‫(( استمارة انخطت انتذريسيت انسىُيت ))‬
‫اسم انتذريسي‪:‬‬
‫د ‪ .‬صالح انذيه ػذوان طً‬
‫انبريذ االنكترَوي ‪:‬‬
‫‪Salahadnan9999@yahoo.com‬‬
‫اسم انمادة‪:‬‬
‫‪Electrical A.C Circuit‬‬
‫مقررا نفصل‪:‬‬
‫أٌذاف انمادة‪:‬‬
‫انتفاصيم االساسيً‬
‫نهمادة ‪:‬‬
‫انكتب انمىٍجيت‪:‬‬
‫‪Study of the electrical A.C circuit &analysis‬‬
‫‪In this section study all of theorem and all the type of A.C circuit‬‬
‫‪with series and parallel and the complex number with resistance,‬‬
‫‪capacitance ,inductors‬‬
‫‪INTRODUCTORY CIRCUIT ANALYSIS BY‬‬
‫‪BOYLESTAD‬‬
‫‪Lessons In Electric Circuits, Volume II – AC‬‬
‫انمصادر انخارجيت ‪:‬‬
‫تقذيراث انفصم‪:‬‬
‫‪By Tony R. Kuphaldt‬‬
‫انفصم انذراسي‬
‫االمتحان األَل‬
‫االمتحان انثاوي‬
‫انمختبراث‬
‫االمتحان انىٍائي‬
‫األَل‬
‫انثاوي‬
‫‪10‬‬
‫‪10‬‬
‫‪15‬‬
‫‪15‬‬
‫‪50‬‬
‫‪50‬‬
‫مؼهُماث إضافيت ‪:‬‬
‫‪1‬‬
‫انمالحظاث‬
‫ي‬
‫انمادة انؼم ل ة‬
‫األسبُع‬
‫جذَل انذرَس األسبُػي – انفصم انذراسي األَل‬
‫انمادة انىظريت‬
1
Representation of A.C circuit
parameter, complex of voltage and
current
Complex impedance and admittance, 2
complex power
3
Series and parallel circuit
Phasor diagrams, solve question
4
Resonance, series ,resonant
frequency
Variation impedance, admittance
&current against frequency
Quality factor & resonant voltage
rise, half power points and
bandwidth
Locus diagrams, impedance,
admittance and current locus
Variable inductance, variable
capacitance
Variable resistance, reactance
variation against frequency
Solution of AC- circuit
5
6
7
8
9
10
11
Superposition theory, Mesh
analysis,
Norton theorem, thevinon theory
12
Maximum power transfer theorem
14
13
15
16
: ‫تُقيغ انؼميذ‬
2
: ‫تُقيغ األستار‬
‫انمالحظاث‬
‫ي‬
‫انمادة انؼم ل ة‬
‫األسبُع‬
‫جذَل انذرَس األسبُػي – انفصم انذراسي انثاوي‬
‫انمادة انىظريت‬
Magnetically-coupled circuit, self
and mutual inductance coils
The Coupling coefficient ,polarity
1
Dot rule, analysis off magnetically
3
2
Coupled circuits
4
Two-port network(T.P.N.)
5
Forms of T.P.N, attenuation
6
Phase function, symmetrical &
unsymmetrical T.P.N.
ELECTIC FILTERS,LOWPASS FILTER&HIGH-PASS
FILTER
BAND-PASS FILTER&BANDSTOP FILTER
PROTO-TYPE ,l,t ANDX
SECTION
M-derived T-section & Mderived X-section
QUESTION & ANSWER
7
8
9
10
11
12
QUESTION & ANSWER
13
QUESTION & ANSWER
14
QUESTION & ANSWER
15
16
: ‫تُقيغ انؼميذ‬
3
: ‫تُقيغ األستار‬
Representation of A.C circuit parameter, complex of
voltage and current
AC Circuits
w
i m wL

im
wC

m

im R
iron


V1
V2
N1
(primary)
4
N2
(secondary)
Phasors


i R  m sin wt
R
Q
  m sin wt
C

i C  wC m cos wt
di L
  m sin wt
dt


i L   m cos wt
wL
• R: V in phase with i
VR  Ri R   m sin wt
• C: V lags i by 90
VC 
• L: V leads i

by 90
VL  L
A phasor is a vector whose magnitude is the maximum value of a quantity (eg V or I)
and which rotates counterclockwise in a 2-d plane with angular velocity w. Recall
uniform circular motion:
x  r coswt
y  r sinwt
The projections of r (on
the vertical y axis) execute
sinusoidal oscillation.
5
y
y
w
x
Suppose:
xx
0,
r1
n
.. r1 Phasors
for L,C,R
11

V
i
R
V
f(
f( xx))000
VR  Ri m sinwt
xx
r1
00,, r1 ..
.. r1
r1
nn 11
00
22
4
6
x
xx
f( x ) 00
V
r1
0 , .. r1
n 1
wt
C
V
2
4
x
V
f( x ) 0
0
V
1
0
0
6
L
2
4
x
C
66
i
1.01
w
i
0
1.01 1
VL  wLi m cos wt
R
t
i
1
i m cos wt
wC
w
wt
11
VC  
i
6
6.28
L
w
i
wt
Complex impedance and admittance, complex
power
Series LCR
AC Circuit
R
•
Back to the original problem: the loop
equation gives:
L
7
d 2Q
dt 2

Q
dQ
R
  m sin wt
C
dt
C


L
•
Assume a solution of the form:

Here all unknowns, (im,) , must be found from the loop eqn; the initial conditions
have been taken care of by taking the emf to be:   m sinwt.
•
To solve this problem graphically, first write down expressions
for the voltages across R,C, and L and then plot the appropriate
phasor diagram.
i  i m sin(wt  )
Phasors: LCR
• Given:    m sin wt
• Assume:
R

C
L



w
i m wL

From these equations, we can draw the phasor
diagram to the right.

This picture corresponds to a snapshot at t=0. The
projections of these phasors along the vertical axis
are the actual values of the voltages at the given
time.

im
wC
8

m

im R
Phasors: LCR
w
i m XL
R
C


m

L


i m XC
•
im R
The phasor diagram has been relabeled in terms of the
reactances defined from:
X L  wL
XC 
1
wC
The unknowns (im,) can now be solved for
graphically since the vector sum of the voltages
VL + VC + VR must sum to the driving emf .
9
Lecture 20, ACT 3

A driven RLC circuit is connected as shown.
For what frequencies w of the voltage
source is the current through the resistor
largest?
(a) w small (b) w large (c) w 
10

R

w
1
LC
C
L
Conceptual Question

A driven RLC circuit is connected as shown.
For what frequencies w of the voltage
source is the current through the resistor
largest?
1
w

(c)
(b)
w
large
(a) w small
LC

R

w
C
• This is NOT a series RLC circuit. We cannot blindly apply our
techniques for solving the circuit. We must think a little bit.
• However, we can use the frequency dependence of the impedances
(reactances) to answer this question.
• The reactance of an inductor = XL = wL.
• The reactance of a capacitor = XC = 1/(wC).
• Therefore,
• in the low frequency limit, XL  0 and XC   .
• Therefore, as w  0, the current will flow mostly through the
inductor; the current through the capacitor approaches 0.
• in the high frequency limit, XL   and XC  0 .
• Therefore, as w  , the current will flow mostly through the
capacitor, approaching a maximum imax = /R.
11
L
Series and parallel circuit
Resistive Elements
12
Impedance of the Resistor
13
Inductive Reactance
14
Capacitive Reactance
15
Series Configuration
16
Phasor diagrams, solve question
i m XL
m




i m XC
X L  wL
tan  
1
wC

m
im R
XC 
im R
i m (XL -X C)
X L  XC
R

 2m  i 2m R 2   X L  XC 
2


Z  R 2   X L  XC 
17
2
im 
m
R 2   X L  XC 
2

m
Z
Phasors:Tips
i m XL
y
• This phasor diagram was drawn as a
snapshot of time t=0 with the voltages
being given as the projections along the
y-axis.
• Sometimes, in working problems, it is
easier to draw the diagram at a time when
the current is along the x-axis (when i=0).
m



i m XC
imXL
x
im R
m

imR
imXC
“Full Phasor Diagram”
18
From this diagram, we can also create a
triangle which allows us to calculate the
impedance Z:
Z
X L  XC

R
“ Impedance Triangle”
Phasors:LCR
Phasors:LCR
We
We have
have found
found the
the general
general solution
solution for
for the
the driven
driven LCR
LCR circuit:
circuit:
ii 
sin(wt  )
 ii m
m sin(wt  )
iimX
L
mXL
 m
m


w
w
iimR
mR
iimX
C
mXC
the
the loop
loop
eqn
eqn


 
i
Z
 im
mZ
 m
m
ii m 
m Z
Z
X
XLL
Z
Z
X
 wL
XL
L  wL


1
1
X

XC

C wC
wC
Z
 X 
Z
 R 
  X
XL
L  XC
C
R 22
19
X

XL
X
XC
L
C
tan


tan  
R
R
2
2
X
XCC
X
XLL -- X
XCC
R
R
Lagging & Leading
The phase  between the current and the driving emf depends on the
relative magnitudes of the inductive and capacitive reactances.
im
X L  wL
1
XC 
wC
X  XC
tan   L
R

 m
Z
XL
Z
XL
XL


R
XC
XL > XC
>0
current
LAGS
applied voltage
20
Z
R
Z
XC
XL < XC
<0
current
LEADS
applied voltage
R
XC
XL = XC
=0
current
IN PHASE
applied voltage
Conceptual Question

The series LCR circuit shown is driven by a
generator with voltage  =  msinwt. The time
dependence of the current i which flows in the
circuit is shown in the plot.
How should w be changed to
1A bring the current and driving
voltage into phase?
(b) decrease w
(a) increase w
(c) impossible
1B • Which of the following phasors represents the current i at t=0?
(c)
(b) i
(a)
i
i
21
Resonance, series ,resonant frequency
Resonance

For fixed R,C,L the current im will be a maximum at the resonant frequency w0
which makes the impedance Z purely resistive.
ie:
im 
m

Z
m
R 2   X L  XC 
reaches a maximum when:
2
X L  XC
the frequency at which this condition is obtained is given from:
1
1
woL 
 wo 
w oC
LC
22
•
Note that this resonant frequency is identical to the natural
frequency of the LC circuit by itself!
•
At this frequency, the current and the driving voltage are in
phase!
X  XC
tan   L
0
R
Resonance
The current in an LCR circuit depends on the values of the elements and
on the driving frequency through the relation
im 
im 
m

Z
m
R 2   X L  XC 
m
1

 m cos 
R 1  tan 2 
R
Suppose you plot the current versus w, the
source voltage frequency, you would get:
2
x
0.0,
m
1
R0
r1
.. r1
n
R=Ro
f( x )
im0.5
g( x )
R=2Ro
00
23
00
1
wx
2o
2w
24
25