Sample problems
Topic: RC and RL circuits
Statement of problem
The switch in the circuit in the figure has been in position a for a long time.
8
mA
27
k
Ω
33
k
Ω
a
b
0
t
=
0.25
F
μ
3
k
Ω
2
k
Ω
4
k
Ω
0
i
At t=0, the switch is thrown to position b.
(a) Find
0
( )
i
t
for t>0.
(b) What percentage of the initial energy stored in the capacitor is dissipated in the
4
k
Ω
resistor
250
s
μ
after the switch has been thrown?
Solution
(a) Prior to t=0, the circuit looks like
8
mA
27
k
Ω
33
k
Ω
a
0.25
F
μ
First, the initial voltage on the capacitor is calculated by KVL
(0)
8
(27
/ /33
)
118.8
c
v
mA
k
k
V
=
×
Ω
Ω =
Then after t=0, the circuit looks like
b
0.25
F
μ
3
k
Ω
2
k
Ω
4
k
Ω
0
i
(0)
C
v
+
−
The time constant for the RC circuit is
(3
/ /(2
4
))
0.25
0.5
k
k
k
F
ms
τ
μ
=
Ω
Ω +
Ω
×
=
Therefore, for t>0, the voltage on the capacitor is
( )
(0)exp(
/
)
118.8exp( 2000 )(
)
c
c
v
t
v
t
t
V
τ
=
−

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