Chapter 21 continued
CHAPTER
Challenge Problem
Current Electricity
——
page 579
The plates of a capacitor attract each other because they
cariy opposite charges. A capacitor consisting Of two parallel
plates that are separated by a distance, d, has capacitance C.
1
, .
Practice Problems
22.1
—
F=Eq,E
andVt
F=Eq=()q(
page 598
For all problems, assume that the battery volta
ge and
lamp resistances are onstant, no matter what
current
is present.
Current and Circuits
pages 591—600
pae 594
The current through a lightbulb connected
across the terminals of a 125N outlet is
0.50 A. At what rate does the bulb convert
electric energy to light? (Assume 100 perc
ent
efficiency,)
d
C
g
p
2 What charge must he stored on a 22rI capacitor to have a lime of 20
between the plates if they are separated by 1 5 mm?
=
iv
(Q5O A)(125 V)
=
=
63 J/s
=
63 W
.
F
so q
Z A car battery causes a current of 2.0
A
through a lamp and produces 1 2 V across
it. What is the power used by the lamp?
Cd
=
=
=
p= IV=(2.OA)(12 V)=24W
3
.5X10 m)
5
\/(2.O N)(2
2X1O 9(1
3 What is the current through a 75W
lightbulb that is connected to a 125-V outlet?
p= iv
4
2.6X
10 C
75W
125V
I
I
)
0
0
4. The current through the starter moto
r of a
car is 210 A. lfthe battery maintains 12 V
across the motor, how much electric energy
is delivered to the starter in O.() s?
p= IVand E= Pt
Thus, E
C
=
=
r
I
444
Solutions Manual
‘
_w
Derive an expression for the force bewcecn the two
plates when the capacitor has chargc ci.
Combine the following equations:
q
,
i SiCS Prmciplcs nd Problems
1
R
iVt
(210 A)(12 V)(1OO s)
25X1O J
4
I
PIysics:
0.90W
3.OV
frincip]cs
Y
I
I
7.1
12V
33i
1?
,36
A motor with an operating resistance of
32 11
is connected to a oltage souue. 1 he urren
t
in the circuit is 3.8 A. What is the voltage
of
the source
V
=
IR
—
(38 A)(32
c)
=
2
t2x
10 V
8. A sensor uses 2.O’c 1()
A of current when
it is opeiated by a 3.0-V batter. What is
the
resistance ot th sensoi circuit?
R=
=
4
15x
f
1O
4
OX
A
1O
9. A lamp draws a current of 0.50 A when
it is
connected to a 120-V source.
a What is the resistance of thc lamp?
1?
=
=
:
2
24X
1O
=
b. What is the l)owCY consumption of the
larnp
=
5 A flashlight bulb s rated at 0.90 XV. If
the
lightbulh drops 3.0 V, how much current
goes through it?
P= IV
I
6. An automobile panel lamp with a resis
tance
of 33 fl is plated atross a I 2-V battery.
What is the current through the circuit?
and Problems
P
=
IV
=
(O5O A)(120 V)
1
&0X
10 W
1o A 79-\’V lamp is conneued to 125 V.
a. ‘vvhat is the current through the lamp
?
I
75W
125V
1;
060A
b. ‘Vhat is the rcsistance of the lamp?
R=
‘
=
2
=2
Q
1X1O
So!utjon.s \1azual
445
Chapter 22 tIUCd
Chapter 22 continued
1i A resistor is added to the tamp in the previ
ous problem to reduce the current to half of
its original va1ue
Section Review
1
p
=
22.1
2
P
=
a. What is the potential difference across
the lamp’
The new value of the current is
R—
0.60A =0.
30A
2
V = IR
=
—
2 II)
(0.30 A)(2.1 X10
1
6.3
X10 V
=
b. how much resistance was added to the
circuit”
y
=
Current and Circuits
pages 59 1—600
page 600
17. Schematic Draw a schematic diagram
of a
circuit that contains a battery and a light
bulb. Make sure the lighthulb will light
in
this circuit.
4.5V
0,085A
14. Add a voltmeter to measure the potential
difference across the resistors in problems 12
and 13 and repeat the problems.
Both circuits will take the following form.
Therefore,
Rtotai
Riamp
2
4.2X
10
—
Because the ammeter resistance is
assumed zero, the voltmeter readings
will be 60.0 V for Practice Problem 12 and
4.5 V for Practice Problem 13.
2
2.1X
10 1
2
2.1X
10 11
=
How much power is now dissipated in
C.
the lamp?
P
=
IV
=
15.
(0.30 A)(6.3X10” V)
=
19W
Draw a circuit using a hattery a lamp, a
potentiometer to adjust the lamp’s bright
ness, and an on off switch.
Lamp
page 600
12. Draw a ircuit diagatn to include a 60.() V
battery, an ammeter, and a resistance of
12.S 1 in series. Indicate the ammeter read
ing and the direction of the current.
Batt
Switch
16.
I
18. Resistance Joe states that becaus
eR
V/I,
if he increases the voltage, the resistan
ce
will increase. Is Joe correct? Explain.
No, resistance depends on the device.
When V increases, so will!.
19. Resistance You want to measure the
resis
tance of a long piece of wire, Show how
you
would construct a circuit with a battery,
a
voltmetei; an ammeter, and the wire to be
tested to make the measurement. Specir
what you would measure and how you
would compute the resistance.
21. Energy A circuit converts 2,2X
10 J of
energy when it is operated for 3.0 mm
.
Determine the amount of energy it will
convert when it is operated for 1 h.
=
(J
=
4
4.4
X10 J
V
F?
—
Practice Problems
22.2
Using Electric Energy
pages 601—605
page 603
23. A 15-f’ electric heater operates on
a 120-V
outlet,
a. What is the current through the heate
r?
lv
I
Y
‘
R
15[l
b. How much energy is used by the hea
ter
in 30,0 s?
potentiometer
Repeat the previouS prohlem adding an
ammeter and a voltmeter across the lamp
Solutimn ,\lLnnalI
=
I
R
2
t
=
(8.0 (
2
A
15
) fl)(30.0 s)
4
2..9
x10 J
c. How much thermal energy is libe
rated
in this time?
=
.OV.480A
0
6
12.511
Measure the current through the wire
and the potential difference across it.
Divide the potential difference by the
current to obtain the wire resistance.
13. Draw a seriesCir( uit diagram showing a
45V battery, a resistor, and an ammeter
that reads $5 mA. Determine the resistance
and label the resistor Choose a direction
for the çOflVCfltjOfldl current and indicate
the positive telminal of the battery.
446
)(6o.o mm)
22. Critical Thinking We say that pow
er is
“dissipated” in a resistor. To dissipate is
to
use, to waste, or to squander. What is “use
d”
when charge flows through a resistor?
The potential energy of the charges
decreases as they flow through the res
is
tor. This decrease in potential energy
is
used to produce heat in the resistor.
E
—
1 =16W—12W=4.OW
P
4.0 W increase
+
—
Rres
2
P
E
The total resistance of the circuit
is now
125V 2
V
=4.2X10
Rtotai
ob A
1 /
vIR
2
=
12
(1
fl=
2
12
V
W
)
VIR = (12 2
V
1
9.0
)
= 16W
2 Power A circuit has 12 fl of resi
stance and
is connected to a 12-V battery. Determine
the change in power if the resistance
decreases to 9.0 L
PhysicS: Prfn ipics and Problems
Physics: PrincipIe’ and [‘rc blenis
2.9X10 J, because all electric energy
4
is converted to thermal energy.
24. A 39-a resistor is connected across
a 45-V
battery.
a. What is the current in the circuit?
V
45V
F?
3911
Solutwim Pvlanuai
447
Chapter 22 continued
b. flow much energy is used by the resistor
iii .0 mm?
V
2
E F?
—
—
=
‘ ‘5 0 min)(60 s/mm)
(39.)
4
t6X1
0J
Pt
(0.22)(1 00.0 J/s)(1 .0 mm)
(60 s/mm)
3
1.3X
J
10
b. I low many joules of thermal energy does
tho lighth lb produ e each minute?
E
=
Pt
=
(0.78)(1 00.0 J!s)(1 .0 mm)
(60.0 sImm)
=
26.
3
4.7X
10 J
[he resistance of an electric stove element at
0th rating temperature is 11
a. II 220 V are applied across it, what is
the current through the stove element?
22QV A
1
=20
X10
llfl
F?
I low mudi energy does the element
convert to thermal energy in 30.0 s?
V
b
E
=
=
I
R
2
t
=
(1l fl)(30.0 s)
2
1
(2.0X
10 A)
5
1.3X
10 J
c
I he element is used to heat a kettle contaming 120 kg of water. Assume that
(3 percent of the heat is absorbed by
the water. \\ hat is the water’s increase
in temperature during the 30.0 s?
0
mC.T with 0= 0.65E
O.65E
mC
17°C
448
SelUIiufl’ 1arnIa1
Chapter 22 continued
take to charge the battery using a current of
7.5 A? Assume that the charging voltage is
the same as the discharging voltage.
Echarge = (1,3)IVt
=
E= lVt= I(2V)()
=
For a given amount of energy, doubling
the voltage will divide the time by 2.
25. \ I000W iighthulb is 22 percent efficient.
1 his mc ills that 22 percent of the electric
energ is onvertcd to light energy.
a. I los many joules does the lightbulb
co wert to light each minute it is in
opec luon?
E
27. A I 20-V water heater takes 2.2 h to heat a
given volume of water to a certain tempera
ture. How long would a 240-V unit operating
with the same current take to accomplish
the same task?
=
(1.20 kg)(418O JIkg°C)
=1.lh
t=
t
—
31.
page 605
28. An electric space heater draws 1 3.0 A horn a
120 V source, ft is operated on the average,
for 5.0 h each day.
a. how much power does the healer use?
=
270 kWh
c. At $0.12 per kwh, how much does it
cost to operate the heater for 30 days?
($0.12/kWh)(270 kWh)
Cost
=
$32.40
29. A digital clock has a resistance of 12,000 i
and is plugged into a 11 °-\‘ outlet.
a. How much current does it draw?
1ISV 3
=96X10’
A
12,000i
F?
b. How much power does it rise?
-
3
.6X10 A) = 11 W
(115 V)(9
c. If the owner of the clock pays $0 12 per
kwh, how much does it cost to operate
the clock for 30 days?
P
=
VI
Cost
=
=
=
X10” kWh)($0.12/kWh)
(1 1 3
(30 days)(24 hlday)
$010
30. An automotive battery can deliver 55 A at
12 V for 1.0 h and requireS 1.3 timeS as
much energy for recharge due to its lessthan-perfect efficiency. I low long will it
Physics Pi’ine iflc c and I roblems
—
858Wh
(7.5A)(12V)
—
Rework the previous problem by assuming
that the battery requires the application of
14 V when it is recharging.
Echarge
=
(1.3)IVt
=
(1 .3)(55 A)(1 2 V)(1 .0 h)
858 Wh
=
t
P= IV= (15.OA)(120V)
1800W = 1.8kW
b. I low much energy in k\Vh does it con
sume in 10 clays?
Pt = (1.8 kW)(5.0 h/day)(30 days)
E
E
IV
(1 .3)(55 A)(1 2 V)(1 .0 h)
858 Wh
—
E
IV
—
858Wh
(7.5 A)(14 V)
82h
—
Section Review
22.2
Using Electric Energy
pages 601—605
page 605
32. Energy A car engine drives a generator,
which produces and stores electric charge in
the car’s battery. The headlamps use the dcc
tric charge stored in the car battery. List the
forms ofenergy in these three operations.
Mechanical energy from the engine
converted to electric energy in the gen
erator; electric energy stored as chemi
cal energy in the battery; chemical
energy converted to electric energy in
the battery and distributed to the headlamps; electric energy converted to
light and thermal energy in headlamps.
1
P
“‘2
_
/R
2
V
V
1
2
1
R
_
1
(0.5
1
2
)
R
V
2
V
_
25
35. £ffidency Evaluate the impact of research
to improve power transmission lines on
society and the environment
Research to improve power transmis
sion lines would benefit society in cost
of electricity. Also, if less power was
lost during transmission, less coal and
other power-producing resources
would have to be used, which would
improve the quality of our environment.
36. Voltage ‘WhY sould an ehectik range and
an electric hot wner heater he connected to
a 240-V circuit rather than a I 20 V circuit?
For the same power, at twice the voltage, the current would be halved. The
R loss in the circuit wiring would be
2
1
dramatically reduced because it is proportional to the square of the current.
37. Critical Thinking Whcn demand for elec
tric power is high, power
ompanies some
times reduce the voltag
e, thereby producing
a °brown-out” What is
being saved?
Power, not energy; most devices will
have to run longer.
Chapter Assessment
Concept Mapping
page 610
38. Complete the corn ept rn ip using the fol
lowing terms. watt, cui rent, resistance.
33. Resistance A hair dryer operating from
1 20 V has two settings, hot and warm. In
which setting is the resistance likely to be
smaller? Why?
Hot draws more power, P = IV, so the
fixed voltage current is larger. Because
I = VIR the resistance is smaller,
34. Power Determine the power change in
a
circuit if the applied voltage is decreased by
one- half,
Physics: Principles and Problems
Sviunon.s Manual
449
Chapter 22 continued
Chapter 22 continued
63. Refer to Figure 2245 to answer the fo1low
ing questions.
Motor
57_ What is the effect on the current in a circuit
if both the voltage and the resistance are
doubled? Explain.
No effect V = IF?, so I = VIR and if the
voltage and the resistance both are
doub’ed, the current will not change.
1.5 A
E
N
27 V
V
58W. Ohm’s Law Sue finds a device that looks
lIke a resistor. When she connects it to a
I 5-V batter’ she measures only 45 )< 6 A,
but when she uses a 3.0-V battery, she mea
suE 2 X 10 A. Does the device obey
()lm’s law?
No. V =
IR so R
=
V/L At 1 £
S
b. Ilow much energy is converted if the
motor runs for 15 mm?
At 3.0 !, R
=
A
3
25X10
Pt = (18 W)(15 min)(60 s/mm)
=
120 f
A device that obeys Ohm’s law has a
resistance that is independent of the
applied voltage.
—
J
4
i6X10
9.0 fl
Figure 2245
a. What should the ammeter reading be?
62. Refer to Figure 22-14 to answer the following questions.
c how much power is delivered to the
resistor?
vi
=
=
(27 V)(3O A)
81 W
=
E
=
Pt
=
(81 W)(3600 s)
=
22.1 Current and Circuits
S
Figure 22-14
VI
=
(27 V)(L5 A)
—
41 W
d. How much energy is delivered to the
resistor per hour?
E = Pt
—
(41 W)(3600 s)
=
5J
1.5X10
A nou is (( i wcted to a 1 2-V battery as
shown in Figure 2243.
SL11z;tuns
?IaIzz1al
9.0 V
18 fl
The definition of power is P
,
so
E= Pt
a Figure 22-16
=
1 W)(Q(Rs
(6Ox1O
I
/\man
\
=
18,000J
=
J
4
tBXIO
IV = (210 A)(12 V)
or 25X1O
3 JIs
—
—
2500 JIs
P= 2.5x10
W
3
a. What should the ammeter reading be?
I
=
V/R
=
=
O5O A
Ii. What should the voltmeter reading be?
=
VI
69. Dryers A 4200-’vV clothes dryer is connect
ed to a 220-V circuit. I low mudi c rent
does the dryer draw?
P= IV
9.0 V
P
Mix cui : Principles afl(! Problems
—
b. What power, in watts, does the motor
use?
c How much power is delivered to the
resistor?
Level 1
4a2
P= IV= (O5OA)(12OV)= 1
6OX1O W
b I low much energy is converted r
51) mm?
P
How much power is delivered to the
resistor?
=
2W
96x1O
a. How many joules of energy does the
battery deliver to the motor each second?
27 V
P
=
4 lamp draws 050 A from a 120A generator.
a. How much power is delivered?
1.5A
pages 611—612
61
67.
Ii. What should the voltmeter reading be?
C.
4J
t6x10
68. A 12V automobile battery is cnnnected to
an electric starter motor The urrer
through the motor is 210 A.
a. What should the ammeter reading be?
=
=
66. Lighibulbs A current of 1.2 A is measured
through a lighthulb when it is con zected
across a I 20 V source. What power is dissi
pated by the bulb?
64 Refer to Figure 22-16 to answer the fo1low
ing questions.
Wires car be placed across the termi
Mastering Problems
IV = (8O A)(120 V)
5J
2.9X10
everywhere in this circuit.
the wire with the smaller resistance
2
V
p
F?
Smaller R produces larger power P
dissipated in the wire, which produces
thermal energy at a faster rate.
=
d. How much energy is delivered to the
resistor per hour?
1= V/R=
(45 W)(3600 s)
=3OA
b. What should the voltmeter reading be?
p
Yes, because the current is the same
r al of a Ga) V battery. One has a high resis
tancc, and the other has a low resistance.
\VhEh wire will produce thermal energy at
a faster rite? Why?
=
P= IV= (i2A)(120V)= t4XIO
W
2
1= VIR=
27 V
59 if the ammeter in Figure 22-4a on page 596
ivue mm ed to the bottom of the diagram,
would the ammeter have the same reading?
Explain
6O Tw
Pt
Figure 22-13
a I low much power is delivered to the
motor?
P = VI = (12 V)(1 £ A) = 18 W
E
=
65. Toasters The current through a toastei th it
is connected to a 2O-V source is O A.
What power is dissipated by the toaster?
P
t5V
4
=33X1O
45x1O
6
R
d How much energy is delivered to tEn.
resistor per hour?
=
(9M V)(O.50 A)
es and ProbIem5
Princi
I
JiP7sics. 1
=
I—
°
4200W
V
220V
19A
4.5 W
Solutions 4anua1