Two Loop RLC Circuit
Given:
11
v
Find:
?
)
0
(
1
I
F
C
7
?
)
0
(
2
I
?
)
0
(
3
mH
L
2
I
5
1
R
?
)
0
(
/
2
dt
dI
8
2
R
?
L
U
7
3
R
?
C
U
?
)
(
2
T
I
?
)
(
3
T
I
The circuit parameters in the diagram above have the following values:
E
= 11 V,
C
= 7 μF,
L
= 2 mH,
R
1
= 5
,
R
2
= 8
, and
R
3
= 7
.
After it has been open for a long time, the switch is closed at
t
= 0.
(a) Find the currents at
t
= 0+. (Current arrows in the circuit diagram define conventions for
positive directions).
(b) At what rate is
I
2
increasing right after the switch is closed?
(c) After the switch has been closed for a long time, how much energy is stored in the inductor?
(d) After the switch has been closed for a long time, how much energy is stored in the capacitor?
(e) After the switch has been closed for a long time, it is opened at time
T
. Calculate the currents
I
2
and
I
3
immediately afterward.(Note: A positive value denotes current traveling in the direction shown
in the diagram.)
Solutions

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