CHAPTER
31
Alternating-Current Circuits
Note:
Unless otherwise indicated, the symbols
I
,
V
,
E
, and
P
denote the rms values of
I
,
V
, and
E
and the average
power.
1*
∙
A 200-turn coil has an area of 4 cm
2
and rotates in a magnetic field of 0.5 T. (
a
) What frequency will
generate a maximum emf of 10 V? (
b
) If the coil rotates at 60 Hz, what is the maximum emf?
(
a
)
E
=
NBA
ω
cos
ω
t
(see Problem 30-8-5)
(
b
)
E
max
=
NBA
ω
= 2
π
NBAf
ω
=
E
max
/
NBA
= 250 s
–1
;
f
=
ω
/2
π
= 39.8 Hz
E
max
= 15.1 V
2
∙
In what magnetic field must the coil of Problem 1 be rotating to generate a maximum emf of 10 V at 60
Hz?
Use Equ. 31–4; solve for
B
B
= 0.332 T
3
∙
A 2-cm by 1.5-cm rectangular coil has 300 turns and rotates in a magnetic field of 4000 G. (
a
) What is the
maximum emf generated when the coil rotates at 60 Hz? (
b
) What must its frequency be to generate a
maximum emf of 110 V?
(
a
)
Use Equ. 31-4
(
b
) Use Equ. 31-4; solve for
f
=
ω
/2
π
E
max
= 13.6 V
f
= 486 Hz
4
∙
The coil of Problem 3 rotates at 60 Hz in a magnetic field
B
. What value of
B
will generate a maximum emf
of 24 V?
Use Equ. 31-4; solve for
B
B
= 0.707 T
5*
∙
As the frequency in the simple ac circuit in Figure 31-26 increases, the rms current through the resistor
(
a
)
increases.
(
b
) does not change.
(
c
) may increase or decrease depending on the magnitude of the original
frequency.
(
d
) may increase or decrease depending on the magnitude of the resistance.
(
e
) decreases.
(
b
)
6
∙
If the rms voltage in an ac circuit is doubled, the peak voltage is
(
a
) increased by a factor of 2.
(
b
)
decreased by a factor of 2.
(
c
) increased by a factor of
2
.
(
d
) decreased by a factor of
2
.
(
e
) not changed.
(
a
)
7
∙
A 100-W light bulb is plugged into a standard 120-V (rms) outlet. Find (
a
)
I
rms
, (
b
)
I
max
, and (
c
) the
maximum power.
(
a
)
Use Equ. 31-14
(
b
)
Use Equ. 31-12
I
rms
= 0.833 A
I
max
= 1.18 A

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