747
Chapter 29
AlternatingCurrent Circuits
Conceptual Problems
1
•
A coil in an ac generator rotates at 60 Hz. How much time elapses
between successive peak emf values of the coil?
Determine the Concept
Successive peaks are onehalf period apart. Hence the
elapsed time between the peaks is
()
ms
.33
8
s
60
2
1
2
1
2
1
1
=
=
=
−
f
T
.
2
•
If the rms voltage in an ac circuit is doubled, the peak voltage is
(
a
) doubled, (
b
) halved, (
c
) increased by a factor of
2 , (
d
) not changed.
Picture the Problem
We can
use the relationship between
V
and
V
peak
to decide
the effect of doubling the rms voltage on the peak voltage.
Express the initial rms voltage in
terms of the peak voltage:
2
peak
rms
V
V
=
Express the doubled rms voltage in
terms of the new peak voltage
peak
V'
:
2
2
peak
rms
V'
V
=
Divide the second of these equations
by the first and simplify to obtain:
2
2
2
peak
peak
rms
rms
V
V'
V
V
=
⇒
peak
peak
2
V
V'
=
Solving for
peak
V'
yields:
peak
peak
2
V
V'
=
⇒
)
(
a
is correct.
3
•
[SSM]
If the frequency in the circuit shown in Figure 2927 is
doubled, the inductance of the inductor will (
a
) double, (
b
) not change, (
c
) halve,
(
d
) quadruple.
Determine the Concept
The inductance of an inductor is determined by the
details of its construction and is independent of the frequency of the circuit.
The
inductive reactance, on the other hand, is frequency dependent.
)
(
b
is correct.
4
•
If the frequency in the circuit shown in Figure 2927 is doubled, the
inductive reactance of the inductor will (
a
) double, (
b
) not change, (
c
) halve,
(
d
) quadruple.
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View Full DocumentChapter 29
748
Determine the Concept
The inductive reactance of an inductor varies with the
frequency according to
.
L
X
L
ω
=
Hence, doubling
will double
X
L
.
)
(
a
is
correct.
5
•
If the frequency in the circuit in Figure 2928 is doubled, the
capacitive reactance of the circuit will (
a
) double, (
b
) not change, (
c
) halve,
(
d
) quadruple.
Determine the Concept
The capacitive reactance of an capacitor varies with the
frequency according to
.
1
C
X
C
=
Hence, doubling
will halve
X
C
.
)
(
c
is
correct.
6
•
(
a
) In a circuit consisting solely of a ac generator and an ideal
inductor, are there any time intervals when the inductor receives energy from the
generator? If so, when? Explain your answer. (
b
) Are there any time intervals
when the inductor supplies energy back to the generator? If so when? Explain
your answer.
Determine the Concept
Yes to both questions. (
a
) While the magnitude of the
current in the inductor is increasing, the inductor absorbs power from the
generator. (
b
) When the magnitude of the current in the inductor decreases, the
inductor supplies power to the generator.
7
•
[SSM]
(
a
) In a circuit consisting of a generator and a capacitor, are
there any time intervals when the capacitor receives energy from the generator? If
so, when? Explain your answer. (
b
) Are there any time intervals when the
capacitor supplies power to the generator? If so, when? Explain your answer.
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 Spring '12
 Goussiou
 Physics, Current

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