Lecture17 Examples
HW175.
(HRW 3120) An oscillating LC circuit has a current amplitude of 7.50 mA, a
potential amplitude of 250 mV, and a capacitance of 220 nF. What are (a) the period of
oscillation, (b) the maximum energy stored in the capacitor, (c) the maximum energy
stored in the inductor, (d) the maximum rate at which the current changes, and (e) the
maximum rate at which the inductor gains energy?
Solution:
20. (a)
From
V = IX
C
we find
ω
=
I/CV
.
The period is then
T
= 2
π
/
ω
= 2
π
CV/I
= 46.1
μ
s.
(b) The maximum energy stored in the capacitor is
27
2
9
11
(2.20 10
F)(0.250 V)
6.88 10 J
22
E
UC
V
−−
==
×
=
×
.
(c) The maximum energy stored in the inductor is also
2
/2
B
UL
I
=
=
6.88 nJ .
(d) We apply Eq. 3035 as
V
=
L
(
di/dt
)
max
. We can substitute
L = CV
2
/I
2
(combining
what we found in part (a) with Eq. 314) into Eq. 3035 (as written above) and solve for
(
di/dt
)
max
.
Our result is
23
2
3
7
max
(7.50 10
A)
1.02 10 A/s
/
(2.20 10
F)(0.250 V)
di
V
V
I
dt
L
CV
I
CV
−
−
×
⎛⎞
=
=
=
×
⎜⎟
×
⎝⎠
.
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 Spring '08
 Kim
 Capacitance, Current, Energy, Inductor, HRW, maximum energy

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