choe (dec865) – Practice HW 18 Solutions – Weathers – (22202)
1
This
printout
should
have
13
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
Initially, the capacitor in a series
LC
circuit
is charged.
A switch is closed, allowing the
capacitor to discharge, and 0
.
3
μ
s later the
energy stored in the capacitor is onefourth
its initial value.
Find the inductance if the capacitance is
3 pF.
Correct answer: 0
.
0273567 H.
Explanation:
Let :
t
= 0
.
3
μ
s = 3
×
10
−
7
s
and
C
= 3 pF = 3
×
10
−
12
F
.
The capacitor charge in an oscillating
LC
circuit is
Q
(
t
) =
Q
max
cos(
ω t
+
φ
)
,
where
ω
=
1
√
L C
.
To determine the phase
angle
φ
in the above equation, we use the
initial condition that, at
t
= 0, the charge is
maximum. Thus
Q
max
=
Q
max
cos
φ
1 = cos
φ
φ
= 0 rad
.
The energy stored in the capacitor at any
given time is
U
(
t
) =
1
2
Q
(
t
)
2
C
.
When the energy is onefourth its initial value,
we find that
U
(
t
) =
1
4
U
(0)
1
2
Q
(
t
)
2
C
=
1
4
parenleftbigg
Q
2
max
2
C
parenrightbigg
Q
(
t
) =
1
2
Q
max
1
2
= cos
parenleftbigg
t
√
L C
parenrightbigg
t
√
L C
= cos
−
1
parenleftbigg
1
2
parenrightbigg
=
π
3
rad
.
Solving for
L
gives
L
=
9
t
2
π
2
C
=
9 (3
×
10
−
7
s)
2
π
2
(3
×
10
−
12
F)
=
0
.
0273567 H
.
002
(part 1 of 3) 10.0 points
An
LC
circuit is shown in the figure below.
The 13 pF capacitor is initially charged by the
16 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
13 pF
16 V
S
b
a
Find the frequency of the oscillations.
Correct answer: 1
.
13973
×
10
6
Hz.
Explanation:
L
C
E
S
b
a
Let :
C
= 13 pF = 1
.
3
×
10
−
11
F
,
L
= 1
.
5 mH = 0
.
0015 H
,
and
E
= 16 V
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
choe (dec865) – Practice HW 18 Solutions – Weathers – (22202)
2
Using the equation
ω
=
1
√
L C
,
the frequency is
f
=
ω
2
π
=
1
2
π
√
L C
=
1
2
π
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Work, Correct Answer, LC circuit, Qmax, Choe

Click to edit the document details