Answer Key
Chapter 23
c. What is the current through each resistor?
1. Three 12.0-! resistors are connected in
series to a 50.0-V power source.
a. What is the equivalent resistance of the
circuit?
! 12.0 ! " 12.0 ! " 12.0 !
! 36.0 !
b. What is the current in the circuit?
V
I
R ! ""
V
R
I ! ""
45.0 V
15.0 !
! 3.00 A
3. Two resistors are connected in series to a
power source. The voltage drop across the
first resistor is 5.40 V and the voltage drop
across the second resistor is 9.80 V. The current through the circuit is 1.20 A.
a. What is the resistance of each of the
resistors?
50.0 V
! ""
36.0 !
V
I
R5.40V ! ""
! 1.39 A
c. What is the voltage drop across each
resistor?
5.40 V
1.20 A
! ""
! 4.50 !
V
I
R ! ""
V
I
R9.80V ! ""
V ! IR
9.80 V
1.20 A
! (1.39 A)(12.0 !)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
V
R
I ! ""
! ""
R ! R1 " R2 " R3
! ""
! 16.7 V
2. Three 15.0-! resistors are connected in
parallel to a 45.0-V power source.
a. What is the equivalent resistance of the
circuit?
1
15.0 !
1
15.0 !
1
15.0 !
! " " " "" " ""
1
5
! "" ! ""
R ! 5.00 !
b. What is the current in the circuit?
V
I
R ! ""
V
R
I ! ""
45.0 V
! ""
5.00 !
! 9.00 A
Physics: Principles and Problems
! 8.17 !
b. What is the equivalent resistance of the
circuit?
R ! R1 " R2
! 4.50 ! " 8.17 !
1
1
1
1
"" ! "" " "" " ""
R
R1
R2
R3
3
15
V
I
R ! ""
! 12.7 !
4. What is the equivalent resistance of the
circuit shown below? What is the current
in the circuit? What is the voltage drop
across the two resistors wired in parallel?
Find the equivalent resistance of the
resistors in parallel.
1
1
1
"" ! "" " ""
Req1
R2
R3
1
12 !
1
12 !
! "" " ""
Req1 ! 6.0 !
Supplemental Problems Answer Key
179
Answer Key
Chapter 23 continued
Using the equivalent resistance of the
resistors in parallel, find the resistance
of the resistors in series.
Req2 ! R1 " Req1
! 88 ! " 6.0 !
6. A 12-! and an 18-! resistor are connected
to a 48-V power source.
a. What is the equivalent resistance of the
circuit if the resistors are connected in
series?
R ! R1 " R2
! 94 !
! 12 ! " 18 !
The current in the circuit:
! 3.0#101 !
V
Req2 ! ""
I
b. What is the equivalent resistance of the
circuit if the resistors are connected in
parallel?
V
Req2
I ! ""
1
1
1
"" ! "" " ""
R
R1
R2
120 V
94 !
! ""
1
12.0 !
1
18.0 !
! " " " ""
! 1.3 A
5
36
The voltage drop across the two
resistors:
! ""
R ! 7.2 !
V
I
Req1 ! ""
! (1.3 A)(6.0 !)
! 7.8 V
88 !
Find the current in the circuit.
Let R be the unknown resistance.
"
120 V
12 !
12 !
Then (9.0 V) ! VR " V24
! (4.0 V) " I(24 !)
$
5.0 V
24 !
I ! "" ! 0.21 A
I
5. A 10.0-! resistor, a 20.0-! resistor, and a
30.0-! resistor are wired in parallel and
connected to a 15.0-V power source. What
is the equivalent resistance of the circuit?
1
1
1
1
"" ! "" " "" " ""
R
R1
R2
R3
1
10.0 !
1
20.0 !
Find the resistance of the second
resistor.
V
I
R ! ""
4.0 V
0.21 A
! ""
! 19 !
1
30.0 !
! "" " "" " ""
11
60
! ""
R ! 5.45 !
180 Supplemental Problems Answer Key
Physics: Principles and Problems
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. A voltage divider is made from a 9.0-V battery. Two resistors are connected in series to
the battery. If one resistor has a resistance of
24 ! and the voltage drop across the other
resistor must be 4.0 V, what is the resistance
of the second resistor?
V ! IReq1
Answer Key
Chapter 23 continued
8. A circuit is constructed, as shown in the
figure below. The voltmeter reads 63.0 V.
a. Which resistor dissipates the most
energy per second?
a. What should the potentiometer be set
at for a total equivalent resistance of
50.0 ! in this circuit?
V
R ! ""
I
V
R
RT ! R1 " R2 " RP
RP ! RT $ R1 $ R2 ! 50.0 ! $
10.0 ! $ 20.0 ! ! 20.0 !
I ! ""
63.0 V
36 !
! ""
b. If the potentiometer is set at 32.0 !,
what would be the current in this circuit?
! 1.8 A
P ! I 2R
! (1.8 A)2R
Thus, the resistor with the highest
resistance will dissipate the most
energy per second. So, the 54-!
resistor dissipates the most energy
per second.
b. What is the voltage of the power source?
V ! IR
! I(R1 " R2 " R3)
! (1.8 A)(42 ! " 36 ! " 54 !)
! 240 V
42 !
V
36 !
RT ! R1 " R2 " RP ! 10.0 ! "
20.0 ! " 32.0 ! ! 62.0 !
Vsource
9.0 V
I! "
! " ! 0.14 A
62.0 !
RT
c. If the potentiometer were turned so that
the resistance increases, what would
happen to the current?
Since the resistors are connected
in series, as RP increases, RT will
increase by the same amount. From
Ohm’s law, we see that as resistance
and current are inversely proportional so as RT increases, the current in the circuit will decrease.
R ! R1 " R2 " R3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. A 10.0-! resistor and a 20.0-! resistor are
connected in series with a potentiometer
and a 9.0-V battery.
V
54 !
9. Three identical resistors are connected in
parallel across a power source. Their equivalent resistance is 8.00 !. What is the resistance of each resistor?
11. A piece of lab equipment must be connected to a standard 6.0-V dry cell. The manual
for the equipment says that this device has
an internal resistance of 0.10 ! and cannot
handle more than 2.5 A of current.
a. What value of resistor can you connect
in series with this device that would
allow it to be connected to the power
source?
From Ohm’s law,
Vsource
6.0 V
! "" ! 2.4 !
RT ! "
I
2.5 A
Let R1 ! R2 ! R3 ! R
RT ! R " Rinternal
1
1
1
1
Then, "" ! "" " "" " ""
R ! RT $ Rinternal ! 2.4 ! $ 0.10 !
R
8
R
R
3
R
! 2.3 !
! ""
R ! 24.0 !
Physics: Principles and Problems
Supplemental Problems Answer Key
181
Answer Key
Chapter 23 continued
b. What three resistors of equal value could you use in series
instead of the single resistor determined in part a?
From part a, RT ! 2.4 !
RT ! 3R " Rinternal
R $R
3
T
internal
R ! ""
2.4 ! $ 0.10 !
! ""
3
! 0.77 !
12. Two resistors are connected in parallel to a 3.0-V power source.
The first resistor is marked as 150 ! but the second resistor is unmarked
and unknown. Using an ammeter, you measure the current passing
through the unknown resistor as 45.0 mA.
a. What is the value of the second resistor?
3.0 V
V
R2 ! " ! ""
! 67 !
$3
I2
45.0#10
A
b. What is the current passing through the 150-! resistor?
3.0 V
V
I1 ! " ! " ! 0.020 A ! 20 mA
R2
150 !
c. What is the total current passing through this power source?
1
1
1
" ! " " "
RT
R1
R2
R R
R1 " R2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(150 !)(67 !)
1 2
! ""
RT ! "
150 ! " 67 !
! 46 !
3.0 V
V
I T ! " ! " ! 0.065 A
RT
46 !
! 65 mA
or
IT ! I1 " I2
! 45 mA " 20 mA ! 65 mA
13. A circuit is constructed, as shown in the figure below:
What is the value of R3?
R1 ! 15
R3
R2 ! 30.0 !
R4 ! 40.0 !
7.5 V
0.20 A
182 Supplemental Problems Answer Key
Physics: Principles and Problems
Answer Key
Chapter 23 continued
V
7.5 V
RT ! " ! " ! 37 !
I
0.20 A
1
1
1
"! " " "
R12
R1
R2
R1R2
(15 !)(30.0 !)
15 ! " 30.0 !
R12 ! " ! "" ! 1.0#101 !
R1 " R2
RT ! R12 " R34
R34 ! RT $ R12 ! 37 ! $ 10.0 ! ! 27 !
1
1
1
" ! " " "
R34
R3
R4
R34R4
(27 !)(40.0 !)
R3 ! "" ! "" ! 9.0#101 !
R4 $ R34
40.0 ! $ 27 !
14. What is the equivalent resistance of the resistors in the
circuit as shown in the figure below?
40.0 !
70.0 !
40.0 !
100.0 !
70.0 !
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
40.0 !
10.0 V
RA ! 100 !
1
1
1
2
" ! " " " ! "
RB
R70
R70
R70
R70
70.0 !
! "" ! 35.0 !
RB ! "
2
2
1
1
1
1
3
"! " " " " " ! "
RC
R40
R40
R40
R40
R40
40.0 !
RC ! "
! "" ! 13.0 !
3
3
RT ! RA " RB " RC
! 100.0 ! " 35.0 ! " 13.0 !
! 148 !
Physics: Principles and Problems
Supplemental Problems Answer Key
183
Answer Key
Chapter 24
1. A 1.20-cm wire carrying a current of 0.80 A is perpendicular to a
2.40-T magnetic field. What is the magnitude of the force on the wire?
F ! ILB
! (0.80 A)(0.0120 m)(2.40 T)
! 0.023 N
2. A 24.0-cm length of wire carries a current and is perpendicular to a
0.75-T magnetic field. If the force on the wire is 1.80 N, what is the
current in the wire?
F ! ILB
F
LB
I ! ""
1.80 N
! """
(0.240 m)(0.75 T)
! 1.0#101 A
3. A 0.50-cm length of wire carries a current and is perpendicular to a
magnetic field, as shown below.
a. What is the direction of the force on the wire?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
According to the third right-hand rule, in which the fingers
of the right hand point in the direction of the magnetic field
and the thumb points in the direction of the conventional
current, the direction of the force on the wire is out of the
page or in the negative z direction.
b. What is the magnitude of the force on the wire?
F ! ILB
! (2.6 A)(0.0050 m)(0.75 T)
! 0.0098 N
"y
"z
$x
26 A →
"x
$z
$y
B ! 0.75 T
184 Supplemental Problems Answer Key
Physics: Principles and Problems
Answer Key
Chapter 24 continued
4. A 4.50-cm length of wire carries a 2.1-A
current and is perpendicular to a magnetic
field. If the wire experiences a force of
3.8 N from the magnetic field, what is
the magnitude of the magnetic field?
8. A doubly ionized particle travels through a
magnetic field, as shown in the figure
below. What is the force experienced by the
particle?
F ! qvB
F ! ILB
! (3.2#10$19 C)(4.1#104 m/s)(1.50 T)
F
B ! ""
IL
! 2.0#10$14 N
3.8 N
! """
(2.1 A)(0.0450 m)
B ! 1.50 T
! 40 T
5. A length of wire carrying a current of 2.0 A
is perpendicular to a 6.5-T magnetic field.
What is the length of the wire if it experiences a force of 2.99 N?
v ! 4.1"104 m/s
F ! ILB
F
IB
L ! ""
2.99 N
(2.0 A)(6.5 T)
! ""
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
! 0.23 m
6. An electron beam is perpendicular to a
0.020-T magnetic field. What is the force
experienced by one electron if the beam has
a velocity of 9.8#103 m/s?
F ! qvB
! (1.60#10$19 C)(9.8#103 m/s)(0.020 T)
! 3.1#10$17 N
7. A proton experiences a force of 6.9#10$15 N
when it travels at a right angle to a 1.35-T
magnetic field. What is the velocity of the
proton?
F ! qvB
9. A positively charged particle travels at a
right angle through a 3.00-T magnetic field
with a velocity of 4.50#105 m/s. If the particle experiences a force of 4.32#10$13 N as
it travels through the magnetic field, what is
the charge on the particle?
F ! qvB
F
vB
q ! ""
$13
4.32#10
N
! """
5
(4.50#10 m/s)(3.00 T)
! 3.20#10$19 C
10. An electron traveling 8.6#107 m/s at a right
angle to a magnetic field experiences a force
of 2.9#10$11 N. What is the strength of the
magnetic field?
F ! qvB
F
qB
v ! ""
F
qv
B ! ""
6.9#10$15
N
! """
$19
(1.60#10
C)(1.35 T)
! 3.2#104 m/s
Physics: Principles and Problems
$11
2.9#10
N
! """"
$19
7
(1.6#10
C)(8.6#10 m/s)
! 2.1 T
Supplemental Problems Answer Key
185