Brannon (blb675) – HW #10 – Shih – (58250)
1
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printout
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have
19
questions.
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before answering.
001
(part 1 of 3) 10.0 points
An
LC
circuit is shown in the figure below.
The 12 pF capacitor is initially charged by the
13 V battery when
S
is at position
a
. Then
S
is thrown to position
b
so that the capacitor
is shorted across the 1
.
5 mH inductor.
1
.
5 mH
12 pF
13 V
S
b
a
Find the frequency of the oscillations.
Correct answer: 1
.
18627
×
10
6
Hz.
Explanation:
L
C
E
S
b
a
Let :
C
= 12 pF = 1
.
2
×
10

11
F
,
L
= 1
.
5 mH = 0
.
0015 H
,
and
E
= 13 V
.
Using the equation
ω
=
1
√
L C
,
the frequency is
f
=
ω
2
π
=
1
2
π
√
L C
=
1
2
π
(0
.
0015 H) (1
.
2
×
10

11
F)
=
1
.
18627
×
10
6
Hz
.
002
(part 2 of 3) 10.0 points
What is the maximum value of charge on the
capacitor?
Correct answer: 1
.
56
×
10

10
C.
Explanation:
The initial charge on the capacitor equals
the maximum charge, so the maximum charge
is
Q
max
=
C
E
= (1
.
2
×
10

11
F) (13 V)
=
1
.
56
×
10

10
C
.
003
(part 3 of 3) 10.0 points
What is the maximum value of current in the
circuit?
Correct answer: 0
.
00116276 A.
Explanation:
From
I
=

ω
Q
max
sin(
ω
t
)
=

I
max
sin(
ω
t
)
,
we see that the maximum current is
I
max
=
ω
Q
max
= 2
π
f Q
max
=
0
.
00116276 A
.
004
(part 1 of 2) 10.0 points
A 0
.
244 H inductor is connected to a capacitor
and a 40
.
4
Ω
resistor along with a 47 Hz,
35
.
5 V generator.
To what value would the capacitor have to
be adjusted to produce resonance?
Correct answer: 46
.
9953
μ
F.
Explanation:
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Brannon (blb675) – HW #10 – Shih – (58250)
2
Let :
f
0
= 47 Hz
,
and
L
= 0
.
244 H
.
From
f
0
=
1
2
π
√
L C
,
the capacitance is
C
=
1
4
π
2
L f
0
2
=
1
4
π
2
(0
.
244 H) (47 Hz)
2
·
10
6
μ
F
1 F
=
46
.
9953
μ
F
.
005
(part 2 of 2) 10.0 points
Find the voltage drop across the resistor at
resonance.
Correct answer: 35
.
5 V.
Explanation:
Let :
V
= 35
.
5 V
.
At resonance,
X
L
=
X
C
. Therefore,
Z
across
the capacitorinductor combination is zero,
and the voltage drop across the resistor is
35
.
5 V.
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 Spring '08
 Turner
 Physics, Alternating Current, Correct Answer, Inductor, Electrical resistance

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