r INTRODUCTION
OHM'S LAW
3-1
3-2
3-3
34
3-5
3-6
ffi
Ohm's Law
Current
Calculating
CalculatingVoltage
CalculatingResistance
of Current,
The Relationship
Voltage,and Resistance
TechnologyTheoryinto Practice
(EWB)
Electronics
Workbench
and
PSpiceTutorialsavailableat
http://www.prenhalLcom/floyd
In Chapter 2, you studied the conceptsof voltage,
culrent, and resistance.You also were introduced to a
basic electric circuit. In this chapter,you will learn
how voltage, current, and resistanceare interrelated.
You will also learn how to analvze a simole electric
circuit.
Ohm's law is perhapsthe single most important
tool for the analysis of electric circuits. There are
many other laws, theorems, and rules-some of which
you can live without; however, you must know and be
able to apply Ohm's law.
In 1826 Georg Simon Ohm found that current,
voltage, and resistanceare related in a specific and
predictable way. Ohm expressedthis relationship with
a formula that is known today as Ohm's law. In this
chapter,you will learn Ohm's law and how to use it in
solving circuit problems. Ohm's law is one of the
basic foundation elementsupon which the rest of your
study and work in electronics will be built.
In the TECH TIP, Section 3-6, you will see how
Ohm's law is applicable to a practical circuit. Visualize the following situation: On the job, you are
assignedto test a resistancebox that has been constructed for use in the lab. The resistancebox provides severaldecadesof resistance(10 Q, 100 O,
1.0 kO, etc.) that are switch selectable.This is a rush
job and the resistancebox is urgently neededin a
product test setup. Checking out the box is simple
enough.All you have to do is measurethe resistance
between the two terminals for each setting of the
selector switch and verify that the resistanceis correct. After connecting the multimeter and selecting the
ohmmeter function, you discover that it is not functioning as an ohmmeter.This is the only meter in the
lab that is available immediately. The boss wants this
done right away, so what do you do?
r TECHnology
Theory
Into
Practice
r CHAPTER
OBfECTIVES
a Calculateresistancein a circuit
tr Explain the proporlional relationship of cunent,
D ExplainOhm's law
o Calculate
currentin a circuit
tl Calculate
voltagein a circuit
IIIST()RICAI,
voltage,and resistance
NOTE
Georg Simon Ohm
1781-1854
Georg Simon Ohm was a physicist
bom in Erlangen, Bavaria, in 1787.
After a long struggleto gain recognition for his work in formulating the relationship of current, voltage (electromotive force), and resistance, he
becamea professor at Nuremburg from 1833 to 1849 and
at Munich from 1849 to 1854. The mathematicalrelationship of the basic electrical quantities that he developed
is known today as Ohm's law and the unit of resistance
is the ohm (Q). Photo credit: Library of Congress,
LC-U5Z62-40943.
70 r
OHM'S LAW
3-1 r OHM,S LAW
Ohm's law describes msthematically how voltage, current, qnd resistence in a circuit
are related. Ohm's law is used in three equivalent forms depending on whi.ch quantity
you need to determine. In this section, you will learn each of theseforms.
After completing this section, you should be able to
r Explain Ohm's law
. Describe how % 1, and R are related
. Express 1 as a function of Vand R
. Express V as a function of 1 and R
. Express R as a function of V and 1
Ohm determined experimentally that if the voltage acrossa resistor is increased,the current through the resistor will also increase; and, likewise, if the voltage is decreased,the
cuffent will decrease.For example, if the voltage is doubled, the current will double. If
the voltage is halved, the current will also be halved. This relationship is illustrated in
Figure 3-1, with relative meter indications of voltage and current.
(a) Less V, less 1
(b) More V,morc I
FIGURE3-1
Effect on the current of changingthe voltagewith the resistanceat a constantvalue.
Ohm's law also statesthat if the voltage is kept constant, less resistanceresults in
more current, and, also, more resistanceresults in less current. For example, if the resistance is halved, the current doubles. If the resistanceis doubled, the current is halved.
This concept is illustrated by the meter indications in Figure 3-2, wherc the resistanceis
increasedand the voltage is held constant.
ia) Less R, more /
ib) More R, less1
FIGURE3-2
Effect on the current of changingthe resistancewith the voltage at a constant value.
OHM'S LAW .
71
Formulafor Current
Ohm's law can be stated as follows:
I=!
R
(3-1)
This formula describeswhat was indicated by the circuits of Figures 3-1 and 3-2. For a
constant value of R, if the value of V is increased, the value of 1 increases; if V is
decreased,1 decreases.Also notice in Equation (3-1) that if V is constant and R is
increased,1 decreases.Similarly, if V is constant and R is decreased,1 increases.
Using Equation (3-1), you can calculate the current if the values of voltage and
resistanceare known.
Formulafor Voltage
Ohm's law can also be stated another way. By multiplying both sides of Equation (3-1)
by R and transposingterms, you obtain an equivalent form of Ohm's law, as follows:
V=IR
(3-2)
With this equation, you can calculate voltage if the current and resistanceare known.
Formulafor Resistance
There is a third equivalent way to state Ohm's law. By dividing both sides of Equation
(3-2) by 1 and transposingterms, you obtain
n = I!
(3-3)
This form of Ohm's law is used to determine resistanceif voltage and current values are
known.
Remember,the three formulas-Equations (3-l), (3-2) and (3-3)-are all equivalent. They are simply three different ways of expressingOhm's law.
:toN3-1
EW
1. Ohm's law defineshow three basic quantities are related.What are thesequantities?
2. Write the Ohm's law formula for current.
3. Write the Ohm's law formula for voltage.
4. Write the Ohm's law formula for resistance.
5. If the voltage across a fixed-value resistor is tripled, does the current increase or
decrease, and by how much?
6. If the voltage across a fixed resistor is cut in half, how much will the current
change?
7. There is a fixed voltage across a resistor, and you measure a current of I A. If you
replace the resistor with one that has twice the resistance value, how much current
will you measure?
8. In a circuit the voltage is doubled and the resistance is cut in half. Would the current increase or decrease. and if so. bv how much?
72 T OHM,S LAW
3_2 . CALCULATING
CURRENT
In this section,you will leurn to use Ohm'slaw to determinecurrent vqlaeswhenyou
know the valaesof voltageand resistance.Youwill ulso seehow to use quuntities
expressed
with metricprefixesin circuit calcalqtions.
you shouldbe able to
ffier completingthis secti.on,
I Calculatecurrent in a circuit
. UseOhm'slaw to find currentwhenvoltageandresistance
areknown
. Use voltageandresistance
valuesexpressed
with metricprefixes
In the following examples,the formula I = V/R is used. In order to get current in amperes,
vou must exDressthe value of voltase in volts and the value of resistancein ohms.
EXAMPLE 3-1
How manyamperesof currentarein the circuit of Figure3-3?
FIGURE3-3
v
100v
Solution
Use the formula I = V/R, and substitute 100 V for V and 22 Q for R.
.1 = ! =
R
l o o Y= 4 . 5 5 - {
22o.
There are 4.55 A of current in this circuit.
Related Problem
EXAMPLE 3-2
IfR is changedto 33 f) in Figure 3-3, what is the current?
If the resistancein Figure 3-3 is changedto 47 Q and the voltage to 50 V what is the
new value of current?
Solution
Substitute V = 50V and R = 4l Q,into the formula I = V/R.
,- = oV = f5fOi V= 1 . 0 6 A
RelatedProblem If V= 5 V andR = 1000f). what is the current?
(kcl and MQ)
LargerUnitsof Resistance
In electronics,resistancevalues of thousandsof ohms or even millions of ohms are common. As you learned in Chapter 1, large values of resistanceare indicated by the metric
systemprefixes kilo (k) and mega (M). Thus, thousandsof ohms are expressedin kilohms
(kQ), and millions of ohms in megohms (MO). The following examplesillustrate how to
use kilohms and megohms when you calculate current.
CALCULATINC
CURRENT .
73
Calculate the current in Fisure 3-4.
+
V -
Solution Rememberthat 1.0 kQ is the sameas 1 x 103f). Use the formula I =V/R
and substitute50 V for V and I x l0r Q for R.
't = ! =
R
50v = 50Y =5oxlo-3A=5omA
1.0kO-txt03O-
@@@@@@mm
Related Problem
Calculate the current in Figure 31if
R is changed to 10 kfl.
In Example 3-3, 50 x l0-'A is expressedas 50 milliamperes(50 mA). This can be
used to advantagewhen you divide volts by kilohms. The current will be in milliamperes,
as Example 3-4 illustrates.
How many milliamperes are in the circuit of Figure 3-5?
V:
Solution
When you divide volts by kilohms, you get cur:rentin milliamperes.
I-Y - 39Y =5.36mA
R
5.6kO
RelatedProblem What is the currentin milliamperesif R is changedto 2.2 kCL?
If volts are applied when resistance values are in megohms, the current is in
microamperes(pA), as Example 3-5 shows.
EXAMPTE
3-5
Determine the amount of cur:rentin the circuit of Fisure 3-6.
FIGURE3-6
v
25V
R
4.1MA
solution Recallthat 43 MQ equals4.7 x l0o f). Substitute25 Y for v and
4.7 x 106Q for R.
I=I=#k=#k=5.32x
1 oA
- 6= 5 ' 3p2A
RelatedProblem what is the currentif v is increasedto 100v in Figure3-6?
EXAMPLE3-6
Change the value of R in Figure 3-6 to 1.8 MQ. What is the new value of current?
Solution
When you divide volts by megohms,you get current in microamperes.
-t
Related Prohlem
of current?
9A
= ! = - ' ! - u - == 1 3 . p
R
1.8MC)
If R is doubled in the circuit of Figure 3-6, what is the new value
LargerUnitsof Voltage(kV)
Small voltages, usually less than 50 V are common in semiconductor circuits. Occasionally, howeveq large voltages are encountered.For example, the high-voltage supply in a
television receiver is around 20,000 V (20 kilovolts, or 20 kV), and transmission voltages
generatedby the power companiesmay be as high as 345,000 V (345 kV). The following
iwo examples illustrate how to use voltage values in the kilovolt range when you calculate current.
EXnA,tpLf g-Z
How much current is produced by a voltage of 24 kY across a 12 kC) resistance?
Solution Since kilovolts are divided by kilohms, the preflxes cancel; therefore, the
current is in amPeres.
24kv 24xl0rv
- v
t=
R= 12ko=-=oo
^^
RelatedProblem Whatis the currentin mA producedby 1 kV acrossa 27 kQ resistance?
EXAMpLE 3-S
How muchcurrentis therethrougha 100MQ resistorwhen50 kV areapplied?
Solution In this case,divide 50 kV by 100 MQ to get the current. Substitute
50 x 103V for 50 kV and 100x 106Q for 100MO.
s0kv - sox-lql/=o'5x10-3A=0'5mA
^r-YR- 10ffi=fr
,;i.O
Remember that the power of ten in the denominator is subtracted from the power of
ten in the numerator.So 50 was divided by 100, giving 0.5, and 6 was subtractedfrom
3, giving 10-3.
@wwffiwww@ffiwffi
RelatedProblem How muchcurrentis therethrougha 6.8 MQ resistorwhen 10kV
are applied?
CALCULATING
VOLTACE -
75
In Problems l-4. calculate1.
l.V=l0VandR=5.6f).
2.V=l00VandR=560O.
3.V=5Vand R=2.2kt|.
4. V = 15 V and R= 4.7 MQ.
5. lf a 4J MQ resistorhas 20 kV acrossit, how much current is there?
6. How much current will l0 kV across2.2kA produce?
3-3 r CALCUTATING
VOLTAGE
In this section, yoa will learn to use Ohm's law to determine voltage velues when
you know the valaes of current end resistance. You will also see how to use quantities expressedwith metric prefixes in circuit calculations. After completing this section, you should be sble to
I Calculate voltage in a circuit
. Use Ohm's law to find voltage when current and resistanceare known
. Use current and resistancevalues expressedwith metric prefixes
In the following examples, the formula V = IR is used. To obtain voltage in volts, you
must expressthe value of 1in amperesand the value of R in ohms.
EXAMPTE
3-9
ln the circuit of Figure 3-7, how much voltage is neededto produce 5 A of current?
FICURE3-7
Solution
Substitute 5 A for l and 100 ft for R into the formula V = IR.
V=IR=(5AX100O)=500V
Thus, 500 V are required to produce 5 A of cunent through a 100 O resistor.
Related Prohlem
current?
In Figure 3-7, how much voltage is required to produce 12 A of
SmallerUnitsof Current(mA and pA)
The following two examplesillustrate how to use current values in the milliampere (mA)
and microampere (pA) ranges when you calculate voltage.
EXAMPLE 3-10
How muchvoltagewill be measuredacrossthe resistorin Figure3-8?
FIGURE3-B
Solution Five milliamperes equals 5 x 10-' A. Substitute the values for / and R into
theformulaV=IR.
V = IR= (5 mA)(56 fi) = (5 x 10-3AX56 O) = 280 x 10-3V = 280 mV
When milliamperes are multiplied by ohms, you get millivolts.
Related Problem How much voltage is measured across R if R = 33 Q and 1 =
1.5 mA in Fieure 3-8?
EXAMPLE 3-11
Supposethat there is a current of 8 pA through a 10 Q resistor. How much voltage is
acrossthe resistor?
Solution Eight microamperes equals 8 x 10-6 A. Substitute the values for l and R
into the formula V = IR.
V = I R = ( 8 p A X l 0 O ) = ( 8 x 1 0 - 6 A X l 0 f ) ) = 8 0 x 1 0 - 6V = 8 0 s . V
.
When microamperesare multiplied by ohms, you get microvolts.
Related Problem If there are3.2pA through a47 Qresistor, what is the voltage
acrossthe resistor?
These examples have shown that when you multiply milliamperes and ohms, you
get millivolts. When you multiply microamperesand ohms, you get microvolts.
(kQ and MQ)
LargerUnitsof Resistance
The following two examples illustrate how to use resistancevalues in the kilohm (kQ)
and megohm (MQ) ranges when you calculate voltage.
3-12
EXAMPLE
The circuit in Figure 3-9 has a current of l0 mA. What is the voltage?
FIGURE3_9
solution Tenmilliamperesequals10 x 10-3A and3.3 kQ equals3.3 x 10'.Q. Substitutethesevaluesinto the formulaV = IR.
V = IR = (10mAX3.3kO) = (10x 10-3AX3.3x 103O; = 33 V
CALCULATINC
r 77
RESISTANCE
Notice that 10-3 and 103cancel. Therefore, milliamperes cancel kilohms when multiplied, and the result is volts.
@@@m@a@a@@@rffil
Related Problem
EXAMPLE 3-13
If the current in Figure 3*9 is 25 mA, what is the voltase?
If there is a current of 50 pA through a 4.1 Mtt resisror,what is the voltage?
Solution Fifty microamperes equals 50 x 10-6A and.4.1 MQ is 4.j x 106O. Substitute these values into the formula V = IR.
V = IR = (50 pA)(4.7 MO) = (50 x t0-6 A)\4.7 x 106e) = 235 V
Notice that 10-6 and 106cancel. Therefore, microamperescancel megohms when multiplied, and the result is volts.
Related Prohlem
3-3
If there are 450 prA through a 3.9 MQ resistor,what is the voltase?
In Problems l-7. calculate V.
r=tAandR= 10f).
:.
2. I=SAandR =470Ct.
3. I=3mAandR:I00O.
'
4. I=25 L+AandR=56O.
0 l - n
5 , I = 2 m A a ^n-dl DR- =1 1
.8kQ.
6. I=5 mAardR=100MQ.
;',=;;;;;';=r;il
8. How much voltage is required to produce 100 mA though 4.7 kA?
9. What voltagedo you need to cause3 mA of current in a 3.3 kQ resistance?
10. A battery produces 2 A ofcurent into a 6.8 f2 resistive load. What is the battery
voltage?
r CALCULATING
RESISTANCE
In this section, you will leqrn to use Ohm's Isw to determine resistance values when
you know the vulues of current and voltage. You will ulso see how to use quantities
expressedwith metric prefixes in circuit calculations.
After completing this section, you should he uble to
I Calculate resistance in a circuit
. Use Ohm's law to find resistancewhen voltage and current
are known
. Use current and voltage values expressedwith metric prefixes
In the following examples,the formula R = v/I is used. To get resistancein ohms, you
must expressthe value of 1 in amperesand the value of V in volts.
7B T OHM,S LAW
EXAMPLE 3-14
is neededto draw3.08A of current
In the circuit of Figure3-10, how muchresistance
from the battery?
F I G U R E3 - 1 0
12v for v and3,08A for l intotheformulaR = v/1.
solution Substitute
l2v =3.90c)
p=!1 3.08A
Related Problem
5.45A?
In Figure 3-10, to what value must R be changed for a current of
SmallerUnitsof Current(mA and pA)
The following two examplesillustrate how to use current values in the milliampere (mA)
and microampere (pA) ranges when you calculate resistance.
3-15
EXAMPLE
Supposethat the ammetef in Figure 3-1 I indicates 4.55 mA of current and the voltmeter reads 150 V. What is the value of R?
F I G U R E3 - 1 1
Solution 4.55 mA equals 4.55 x l0-3 A. Substitute the voltage and current values
into the formula R = V/1.
15ov- =33x103c)=33ko
15ov o-!=
" - I - 4 . 5 5 m A -4 . 5 5 x 1 0 - 3 A
When volts are divided by milliamperes, the resistanceis in kilohms.
Related Problem If the ammeter indicates 1.10 mA and the voltmeter reads 75 Y
what is the value of R?
THE RELATIONSHIP
. 79
OF CURRENT,
VOLTACE,
AND RESISTANCE
EXAMPLE 3-1 6
Supposethat the value of the resistor in Figure 3-11 is changed.If the battery volrage
is still 150 V and the arnmeterreads 68.2 prA, what is the new resistor value?
Solution
for R.
68.2 y.A equals68.2 x 10-6A. SubstituteV andl valuesinto the equation
1 5 0 v - -= 2 . 2 x 1 0 6 o =
R=!=,ttou 2.2MdL
I
68.2pA 68.2x 10-6A
When volts are divided by microamperes,the resistancehas units of megohms.
Related Problem If the resistor is changedin Figure 3-11 so that the ammeterreads
45.5 uA, what is the new resistor value? Assume V = 150 V.
1
sEcTloN3-4
i REVIEW
:i
g
=
Y
In Problems,1-5, calculateR.
l , V = 1 0 V a n dI = 2 . 1 3 A .
2.V=270Vand1=
l0A.
3.V=20kVand1=5.13A.
4. V = 15V and1= 2.68mA.
5 . V = 5 V a n dI = 2 . 2 7 p A .
6. You havea resistoracrosswhich you measure25 Y, andyour ammeterindicates
53.2mA of current.What is the resistor'svaluein kilohms?In ohms?
3-5 r THE RELATIONSH|P
OF CURRENT,
VOLTAGE,
AND RESTSTANCE
Ohm's lsw describeshow current is related to voltage snd resistance, Current und
voltage are linearly proportional; carrent and resistance ure inversely related.
Because voltage is the "driving forcel' it is not dependent on the resistsnce when
used us & source, When it is a voltuge drop, it is directly proportional to the resistance
for a given current.
After completing this section, you should be able to
I Explain the proportional relationship of current, voltage, and resistance
. Show graphically that 1 and V are directly proportional
. Show graphically that 1 and R are inversely proportional
. Explain why 1 and V are linearly proportional
The LinearRelationship
of Currentand Voltage
Current and voltage are linearly proportional; that is, if one is increasedor decreasedby
a certain percentage,the other will increase or decreaseby the same percentage,assuming that the resistanceis constantin value. For example, if the voltage acrossa resistor is
tripled, the current will triple.
3-I2 is increasedto three times its presShow that if the voltage in the circuit of Figure
ent value, the current will triple in value'
EXAMPLE3_17
F I C U R E3 - 1 2
R
4.7ka
Solution With 10V, the currentis
'I - Y R
lov =2.1.3mA
4.7kf2
If the voltageis increasedto 30 Y the cunentwill be
30v =6.38mA
! =r, =
-R
4.7kQ
Thecurrentwentfrom2.|3rnAto6.38mAwhenthevoltagewastripledto30V.
RelatedProblemlfthevoltageinFigure3-|2isquadrupled,willthecurrentalso
quadruple?
A Craph of CurrentVersusVoltage
10 Q, and calculate the current for
Let,s take a constant value of resistance,for example,
to 100 V' The current values obtained are
several values of voltage ranging from 10 V
values versus the v values is shown in Figshown in Figure 3-13(;). rhe-gr-aphof the 1
This graph tells us that a change in volture 3_13(b). Note that it iru ,tiagrrt Hne graph.
current' No matter what value R is' assumug" r"rutt, in a linearly proportiorial changein
will always be a straight line'
ing that R is constant,the iraph of l versus V
1(A)
10v
20v
30v
40v
50v
60v
70v
80v
90v
100v
1A
3A
5A
6A
'7A^
8A
9A
l0A
10
9
8
'7
6
5
A
3
2
1
'r-_ 1v0 c )
(a)
40
(b)
F I G U R E3 - 1 3
=
Graph of cuftent versusvoltagefor R 10 d2'
50
90
100
v(v)
T 81
THE RELATIONSHIP
OF CURRENT,
VOLTACE,
AND RESISTANCE
Example 3-18 illustrates a use for the linear relationship between voltage and current in a resistivecircuit.
Assume that you are measuringthe current in a circuit that is operating with 25 V. The
ammeter reads 50 mA. Later, you notice that the current has dropped to 40 mA.
Assuming that the resistance did not change, you must conclude that the voltage
source has changed.How much has the voltage changed,and what is its new value?
Solution The curent has dropped from 50 mA to 40 mA, which is a decreaseof
207o. Since the voltage is linearly proporlional to the cur:rent,the voltage has decreased
by the same percentagethat the current did. Taking 2OVoof 25 V, you get
Change in voltage = (0.2)(25 V) = 5 V
Subtract this change from the original voltage to get the new voltage.
New voltage = 25 Y - 5 V = 20 V
Notice that you did not need the resistancevalue in order to find the new voltage.
Related Prohlem If the current drops to 0 A under the same conditions statedin the
example, what is the voltage?
Are InverselyRelated
Currentand Resistance
As you have seen, current varies inversely with resistanceas expressedby Ohm's law,
I = V/R. When the resistance is reduced, the current goes up; when the resistance is
increased,the current goes down. For example, if the source voltage is held constant and
the resistanceis halved, the current doubles in value; when the resistanceis doubled, the
current is reduced by half.
Let's take a constant value of voltage, for example, 10 V and calculate the current
for several values of resistanceranging from 10 Q to 100 O. The values obtained are
shown in Figure 3-14(a). The graph of the 1 values versus the R values is shown in Figure 3-14(b).
1(A)
1.0
0.9
0.8
I
10
20
30
40
50
60
70
80
90
100
(a)
1.000
0.500
0.333
0.250
0.200
0.167
0.t43
0.t25
0.111
0.100
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
(b)
F I G U R E3 - 1 4
Graph of current versusresistance
for V = 10 V
80 90 100
R( o )
B2 I
OHM'S LAW
SECTION3-5
REVIEW
1.. What doeslinearly proportional mean?
2. Inacircuit, V=2Y and /= l0 mA. If Vis changedto I V what will lequal?
3. If 1= 3 A at aceftain voltage, what will it be if the voltage is doubled?
4. By how many volts must you increasea 12 Y sourcein order to increasethe current in a circuit by 5OVo?
3-6 r TECHnologyTheory lnto Practice
In this TECH TIP, an existing resistance box that is to be used as part of a test setup
in the lab is to be checked out and modifi.eil. Your task is to modify the circuit so that
it will meet the requirements of the new application. You will have to apply your
knowledge of Ohm's law in order to complete this assignment.
The specifications are as follows:
1. Euch resistor is switch selectabk and only one resistor is selectedat a time.
2. The lowest resistor value is to be 10 {L
3. Each successivelyhigher resist&nce in the switch sequence must be s decsde (10
times) increase over the previous one.
4. The mqximam resistor value must be 1.0 MQ.
5, The maximum voltage &cross any resistor in the box will be 4 V
6. Two additional resistorsare required, one to limit the current to 10 mA + 70Voand
the other to limit the carrent to 5 mA + 10Vowith a 4 V drop.
The ExistingResistorCircuit
The existing resistancebox is shown in both top and bottom views in Figure 3-15. The
switch is a rotary type.
(a) Top view
F I G U R E3 - 1 5
(b) Bottom view
SUMMARY I
83
The Schematic
r From Figure 3-15, determine the resistor values and draw the schematic for the
existing circuit so that you will know what you have to work with. Determine the resistor
numbering from the R labels on the top view.
The Schematicfor the New Requirements
r Draw the schematicfor a circuit that will accomplish the following:
1. One resistor at a time is to be connectedby the switch between terminals I and 2
of the box.
2. Provide switch selectable resistor values beginning with 10 Q and increasing in
decadeincrements to 1.0 MO.
3. Each of the resistors must be selectableby a sequenceof adjacent switch positions
in ascendingorder.
4. There must be two switch-selectableresistors,one is in switch position 1 (shown in
Figure 3-15, bottom view) and must limit the current to l0 mA + 10vo with a 4 v
drop and the other is in switch position 8 and must limit the current to 5 mA + lTTo
witha4Vdrop.
5. All the resistors must be standardvalues with l\Vo tolerance.
r Determine the modifications that must be made to the existing circuit board to meet
the
specifications and develop a detailed list of the changes including resistancevalues,
wiring, and new components.You should number each point in the schematicfor easy
reference.
ATest Procedure
r After the resistancebox has been modified to meet the new specifications,it must
be
testedto seeif it is working properly. Determine how you would test the resistancebox
and what instruments you would use. Then detail your test procedure in a step-by-step
format.
Troubleshooting
the Circuit
r When an ohmmeter is connectedacrossterminals I and 2 of the resistancebox, determine the most likely fault in each of the following cases:
l. The ohmmeter shows an infinitely high resistancewhen the switch is in position 3.
2. The ohmmeter shows an infinitely high resistancein all switch positions.
3. The ohmmeter shows an incorrect value of resistancewhen the switch is in position 6.
1. Explain how you applied Ohm's law to this application assignment.
2. Determine the current through each resistor when 4 v is applied acrossit.
SUMMARY
I Voltage and current are linearly proportional.
r Ohm's law gives the relationship of voltage, current, and resistance.
r Current is directly proportional to voltage.
B4 I
OHM,S LAW
I
Current is inversely proportional to resistance.
I
A kilohm (kQ) is one thousand ohms.
T
A megohm (MA) is one million ohms.
T
A microampere (pA) is one-millionth of an ampere.
I
A milliampere (mA) is one-thousandthof an ampere.
I
I
Use 1= V/R when calculating the current.
Use V = IR when calculating the voltage.
I
Use R = V/I when calculating the resistance.
I
Figure 3-16 is a memory aid for the Ohm's law relationships.
V=IR
,(
,", -_
Y
I
F I G U R E3 _ 1 6
r GLOSSARY
Theseterms are also in the end-of-book glossary.
Linear
Characterizedby a straight-line relationship.
Ohm (O) The unit of resistance.
Ohm's law A law stating that current is directly proportional to voltage and inversely proportional to resistance.
r FORMULAS
(3-1)
I=!
Ohm's law for current
(3-2)
V= IR
Ohm's law for voltage
(3-3)
R=!
Ohm's law for resistance
r SELF.TEST
R
I
Ohm's law statesthat
(a) current equals voltage times resistance
(b) voltage equals current times resistance
(c) resistanceequals current divided by voltage
(d) voltage equals current squaredtimes resistance
)
When the voltage acrossa resistor is doubled, the current will
(d) not change
(b) halve
(c) double
(a) triple
3. When l0 V are applied across a 20 C) resistor, the current is
(a) 10A
(b) 0.5A
(c) 200.4
(d) 2A
4. When there are 10 mA of current through a 1.0 kO resistor, the voltage acrossthe resistor is
(a) 100V
(b) O.lV
(c) 10kV
(d) 10V
If 20 V are applied across a resistor and there are 6.06 mA of current, the resistanceis
(c) 330 a
(d) 3.03 kO
(a) 3.3 ka
O) 33 kO
6. A curent of 250 p.A through a 4.'7 kQ resistor produces a voltage drop of
(a) 53.2V
( b ) 1 . 1 8m V
(c) 18.8V
(d) 1.18V
P R O B L E M ST B 5
7' A resistance
of 2.2MQ is connected
acrossa 1 kV source.Theresultingcurent is approximately
(a) 2.2mA
(b) 0.4s5mA
(c) 45.5p.A
(d) 0.455A
8. How muchresistance
is requiredto limit the currentfrom a l0 v batteryto I mA?
(a) 100a
(b) 1.0kO
(c) t0 o
(d) 10kC)
9. An electricheaterdraws2.5A from a ilO V source.The resistance
of the heatrngelementis
(a) 2'75A
(b) 22.7me
(c) 44 A
(d) 440 f,2
10. The currentthrougha flashlightbulb is 20 mA andthe total battery voltage
is 4.5 V. The reststance of the bulb is
(a) 90 O
(b) 22s a
PROBLEMS
(c) 4.44a
(d) 45 o
More dfficult problems are indicated by an asrerisk (*)
SECTION3-1 Ohm,slaw
1' In a circuit consisting of a voltage source and a resistor, describe
what happensto the cunent
when
(a) the voltage is tripted
(b) the voltage is reduced by 75Vo
(c) the resistanceis doubled
(d) the resistanceis reduced by 35Vo
(e) the voltage is doubled and the resistanceis cut rn half
(f) the voltage is doubled and the resistanceis doubled
2. State the formula used to find l when the varuesof v and R are known.
3. State the formula used to find v when the values of 1 and R are known.
4. State the fomula used to find R when the values of v and l are
known.
SECTION3-2 CalculatingCurrent
5. Determine the cunent in each case:
( a )Y = 5 V R = 1 . 0 4
( b )y = 1 5 V n = 1 0 a
(c)Y=50VR=100Q
(d)y=30VR=t5ka
(e) Y= 250v, R = 5.6 Me
6. Determine the current in each case:
(a) Y= 9Y, R =2.7 kA
(c) Y= 40 V R = 68 kQ
(e)Y=66kyR=l0MO
( b ) y = 5 . 5V R = l 0 k O
(d) y= I kV R =2.2ka
7' A 10 Q resistor is connected acrossa l2Y battery.What is the
cur:rentthrough the resistor?
8' A certain resistor has the following color code: orange, orange,red, gold.
Determine the maximum and minimum curents you should expect to measurewhen a 12
V source is connected
acrossthe resistor.
9' A resistor is connected across the terminals of a 25 V source. Determine
the current in the
resistor if the color code is yellow, violet, orange, silver.
*10' The potentiometer connected
as a rheostat in Figure 3-17 is used to control the cuffent to a
heating element. When the rheostat is adjusted to a value of 8 Q or
less, the heating element
can bum out' What is the rated value of the fuse needed to protect
the circuit if the voltage
across the heating element at the point of maximum cuffent is 100
V and the voltage across
the rheostat is the difference between the heating element voltage and
the source voltage?
F I G U R E3 - 1 7
B6 T OHM,S LAW
SECTION3-3 CalculatingVoltage
11. Calculatethe voltagefor eachvalueof1 andR:
( a )I = 2 A , R = 1 8 O ( b )1 = 5 A , R = 5 6 Q
( c )I = 2 . 5 A , R = 6 8 0 Q ( d ) 1 = 0 . 6 A , R = 4 7a
( e )1 = 0 . 1 A , R = 5 6 0 4
12. Calculatethe voltagefor eachvalueof 1 andR.'
(a)1=1rnA,R=10Q
( b )1 = 5 0 m A , R = 3 3 4
( d ) 1 = 1 . 6m A ,R = 2 . 2 k Q
( c )1 = 3 A , R = 5 . 6 k o
(e)I=250 pA,R=1.0kQ
(g) 1: 8s0 pA, R = 10 MQ
(f) 1=500mA,R=1.5MO
(h) 1= 75 p.A, R = 4'7 a
13. Three amperes of cuffent are measuredthrough a 27 {l resistor connected across a voltage
source. How much voltage does the source produce?
14. Assign a voltage value to each source in the circuits of Figure 3-18 to obtain the indicated
amounts of current.
F I G U R E3 - 1 8
27 kQ
t00Mo
47o,
(c)
15. A 6 V source is connected to a 100 f) resistor by two 12 ft lengths of 18 gage copper wire.
The total resistance is found by adding the resistance of both wires to the 100 Cl resistor.
Determine the followine:
(a) Current
(b) Resistor voltage drop
(c) Voltage drop acrosseach length of wire
SECTION3-4 CalculatingResistance
16. Calculatethe resistance
of a rheostatfor eachvalueof V andI:
( a )V = 1 0 V 1 = 2 A ( b ) V = 9 0 V 1 = 4 5 4
( c )V = 5 0 V / = 5 A ( d ) Y = 5 . 5 V 1 = 1 0 A
( e )V = 1 5 0 Y 1 = 0 . 5 A
17. Calculatethe resistance
of a rheostatfor eachsetof V and1 values:
( a )v = 1 0 k V 1 = 5 A ( b )V = 7 Y , 1 = 2 m A
(c)y=500V,1=250mA (d) y=50Y1=500pA
( e )V = l k V 1 = 1 m A
18. Six volts are appliedacrossa resistor.A currentof 2 mA is measured.
What is the valueof
the resistor?
19. The filamentof a light bulbin the circuitof Figure3-19(a)hasa certainamountof resistance,
represented
by an equivalentresistance
in Figure3-19(b).If thebulb operates
with 120V and
0.8 A of current,whatis the resistance
of its filamentwhenit is on?
F I G U R E3 - 1 9
R (filament)
PROBLEMS r
87
20. A
ceftain electrical device has an unknown resistance.You have available a 12 V battery and
an ammeter. How would you determine the value of the unknown resistance?Draw the necessary circuit connections.
21. By varying the rheostat (variable resistor) in the circuit of Figure 3-20, you can change the
amount of current. The setting of the rheostat is such that the current is 750 mA. What is the
resistancevalue of this setting?To adjust the current to 1 A, to what resistancevalue must you
set the rheostat?What is the problem with this circuit?
FIGURE3-20
22. A 120 V lamp-dimming circuit is controlled by a rheostat and protected from excessivecurrent by a 2 A fuse. To what minimum resistancevalue can the rheostat be set without blowing the fuse? Assume a lamp resistanceof 15 Q.
Section3-5 The Relationshipof Current,Voltage,and Resistance
23. A variable voltage source is connectedto the circuit of Figure 3-21. Start at 0 V and increase
the voltage in 10 V steps up to 100 V. Determine the current at each voltage point, and plot a
graph of V versus L Is the graph a straight line? What does the graph indicate?
FIGURE3-21
+
100f,)
24. I n a c e r t a i n c i r c u i t1, = 5 m A w h e n V = l V . D e t e r m i n e t h e c u r r e n t f o r e a c h o f t h e f o l l o w i n s
voltages in the same circuit:
(a)V=1.5V
(d) Y=4V
(b) V=2v
(c)V=3V
(e) V=10V
25. Figxe 3-22 is a graph of voltage versus current for three resistancevalues. Determine R1, R2,
and R3.
FIGURE3-22
v(v)
BB I
OHM,S LAW
26. Which circuit in Figure 3-23 has the most current? The least cuffent?
(aJ
(c)
FIGURE3_23
*27. Yol are measuring the current in a circuit that is operated on a 10 V battery. The ammeter
reads 50 mA. Later, you notice that the current has dropped to 30 mA. Eliminating the possibility of a resistancechange,you must conclude that the voltage has changed.How much has
the voltage of the battery changed,and what is its new value?
*28. If you wish to increasethe amount of current in a resistor from 100 mA to 150 mA by changing the 20 V source, by how many volts should you change the source? To what new value
should you set it?
29. Plot a graph of current versus voltage for voltage values ranging from 10 V to 100 V in l0 V
steps for each of the following resistancevalues:
(a) 1.0 a
(b) s.0 O
(c) 20 a
(d) 100 C)
EWBTroubleshooting
and Analysis
Theseproblems require your EWB compact disk.
30. Open file PRO03-30.EWB on your EWB disk and determine which one of the three circuits
is not working properly?
31. Open file PRO03-31.EWBand measurethe resistancevaluesof the resistors.
32. Open file PRO03-32.EWB and determine the values of the current and voltage.
33. Open file PRO03-33.EWB and determine the value of the source voltage and the resistance.
34. Open file PRO03-34.EWB and find the problem with the circuit.
r ANSWERS
TO SECTION
REVIEWS
Section3-1
1. Current,voltage,andresistance
2. I=V/R
3. V=IR
4. R=V/I
5. Whenvoltageis tripled,currentincreases
by threetimes.
6. Whenvoltageis halved,curent reducesto one-halfof originalvalue.
7. 0.5A
8. The currentwouldincreaseby four timesif the voltagedoublesandthe resistance
is halved.
Section 3-2
1 . 1 = 1 0V / 5 . 6O = 1 . 7 9A
2.I=r00V/560O=l79mA
3.1=5V/2.2kQ=2.27mA
4. I = 15V14.7MA = 3.19p.A
5. I = 20 kVl4.7MA = 4.26mA
6. I = 10kvl2.2 kA = 4.55A
I 89
ANSWERS
TO SELF-TEST
Section 3-3
1 . y = ( 1 A ) ( 1 0a ) = 1 0v
2. y = (8 ,{)(470A) = 3.76kV
Y= (3 mAX100A) = 396my
Y = (25 pAX56Q) = 1.4mV
V = (2 mA)(1.8ko) = 3.6y
3.
4.
s.
6.
7.
8.
9.
10.
V= (5 mA)(100MO) = s00kV
=22y
Y= (10 pA)(2.2l.4A)
Y= (100mA)(4.1ka) = 479y
Y = (3 mA)(3.3ka) = 9.9y
v = (2 A)(6.8A) = 13.6V
Section 3-4
1 . R = 1 0 V 1 2 . 1 3 A = 4A. 7
2 . R = 2 ' 7 0V / 1 0 A= 2 ' 7A
3.R=20kV/5.13A=3.9kC2
4. R = 15V/2.68mA = 5.6kA
5. R=5Y12.27
p.A=2.2MQ
6. R = 25 Y 153.2
mA = 0.4'7kA = 470 Q
Section 3-5
l. Linearlyproportionalmeansthat the samepercentage
changeoccursin two quantities.
2 .I = 5 m A
3 .1 = 6 A
4. LV=6Y
Section 3-6
1. For the new resistors,R = V/1.
2 . I = 4 V l 1 0 O = 4 0 0m A ; I = 4 Y l 1 0 0 A = 4 0 m A ; 1 = 4 V l t . } k C )= 4 m A ;
I = 4 Y/10 kA = 400 ptA;I = 4 y 1100kQ = 40 p"A;I = 4 VA.0 Me = 4 g.A.
ANSWERS
TO RETATED
PROBLEMS
FOR
EXAMPI-ES
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
3-9
ANSWERS
TOSELF.TEST
1. (b)
9. (c)
3.03A
0.005A
0.005A
13.6mA
21.3p.A
2.66pA
37.0mA
1.47mA
1200V
2. (c)
10. (b)
3-10 49.5mV
3-11 0.150mV
3-12 82.5V
3-13 1755V
3-14 2.20Q
3-15 68.2kO
3-16 3.30MO
3-17 Yes
3-18 0 V
3. (b)
4.(d)
5. (a)
6. (d)
7. (b)
8. (d)