h)
×
U
(kW
.
h)
W
= 4
×
3/4 W
.
h = 0.003 kW
.
h
Cost per kW
.
h = $2663
Recharging cost = 0.027 cents
59
∙∙
A 12-V automobile battery with negligible internal resistance can deliver a total charge of 160 A
⋅
h. (
a
) What

Chapter 26
Electric Current and Direct-Current Circuits
is the total stored energy in the battery? (
b
) How long could this battery provide 150 W to a pair of headlights?
(
a
)
U
=
E
It
(
b
)
t
=
U
/
P
U
= 12
×
160 W
.
h = 1.92 kW
.
h = 6.91 MJ
t
= 1920/150 = 12.8 h
60
∙∙
A space heater in an old home draws a 12.5-A current. A pair of 12-gauge copper wires carries the current
from the fuse box to the wall outlet, a distance of 30 m. The voltage at the fuse box is exactly 120 V. (
a
) What is
the voltage delivered to the space heater? (
b
) If the fuse will blow at a current of 20 A, how many 60-W bulbs can
be supplied by this line when the space heater is on? (Assume that the wires from the wall to the space heater and
to the light fixtures have negligible resistance.)
(
a
) Find
R
Cu
=
ρ
L
/
A
,
L
= 60 m;
V
=
E
–
IR
Cu
(
b
) Find
R
bulb
=
E
2
/
P
= 240
Ω
;
I
bulb
=
V
/
R
bulb
N
= (
I
max
– 12.5)/
I
bulb
R
Cu
= 0.308
Ω
;
V
= (120 – 0.308
×
12.5) V = 116 V
I
bulb
= 116/240 A = 0.483 A
N
= 15 bulbs
61*
∙∙
A lightweight electric car is powered by ten 12-V batteries. At a speed of 80 km/h, the average frictional force
is 1200 N. (
a
) What must be the power of the electric motor if the car is to travel at a speed of 80 km/h? (
b
) If each
battery can deliver a total charge of 160 A
⋅
h before recharging, what is the total charge in coulombs that can be
delivered by the 10 batteries before charging? (
c
) What is the total electrical energy delivered by the 10 batteries
before recharging? (
d
) How far can the car travel at 80 km/h before the batteries must be recharged? (
e
) What is
the cost per kilometer if the cost of recharging the batteries is 9 cents per kilowatt-hour?
(
a
)
P
=
Fv
(
b
)
Q
=
It
(
c
)
W
=
Q
E
(
d
)
W
=
Fd
(
e
)
Cost = $0.09(
E
It)
/1000
P
= (1200
×
22.2) W = 26.7 kW
Q
= (160
×
10
×
3600) C = 5.76 MC
W
= 69.1 MJ
d
= 57.6 km
Cost/km = (0.09
×
120
×
160/10
3
)/57.6 = $0.03/km
62
∙∙∙
A 100-W heater is designed to operate with an emf of 120 V. (
a
) What is its resistance, and what current does
it draw? (
b
) Show that if the potential difference across the heater changes by a small amount
∆
V
, the power
changes by a small amount
∆
P
, where
∆
P
/
P
≈
2
∆
V
/
V
. (
Hint:
Approximate the changes with differentials.) (
c
)
Find the approximate power dissipated in the heater if the potential difference is decreased to 115 V.
(
a
)
I
=
P
/
V
;
R
=
V
/
I
(
b
)
P
=
V
2
/
R
;
∆
P
= (
dP
/
dV
)
∆
V
(
c
) Find
∆
P
;
P
=
P
0
+
∆
P
I
= 100/120 A = 0.833 A;
R
= 144
Ω
∆
P
= (2
V
/
R
)
∆
V
= 2
P
(
∆
V
/
V
);
∆
P
/
P
= 2
∆
V
/
V
∆
P
≅
–8.33 W;
P
≅
91.7 W
63
∙
Two resistors are connected in parallel across a potential difference. The resistance of resistor A is twice that
of resistor B. If the current carried by resistor A is
I
, then what is the current carried by B?
(
a
)
I
(
b
)
2
I
(
c
)
I
/2
(
d
)
4
I
(
e
)
I
/4
(
b
)
64
∙
Two resistors are connected in series across a potential difference. Resistor A has twice the resistance of
resistor B. If the current carried by resistor A is
I
, then what is the current carried by B?
(
a
)
I
(
b
)
2
I
(
c
)
I
/2
(
d
)
4
I
(
e
)
I
/4
(
a
)

Chapter 26
Electric Current and Direct-Current Circuits
65*
∙∙

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- staff
- Current, Electric Fields, Electrostatics, Resistance, Static Equilibrium, Resistor, Direct-Current Circuits