Problem 6.57 Repeat Problem 6.56, but this time assume that the switch had been
closed for a long time and then opened at t = 0.
i2
Rs
Vs
t=0
+
_
R
C2
C1
Figure P6.57 Circuit for Problems 6.56 and 6.57.
Solution:
Rs
R
+
Vs _
+ −
υC1(0 )
_
+
_
υC2(0−)
(a) At t = 0−
At t = 0− (Fig. (a)):
Both capacitors act like open circuits. Hence,
υC1 (0) = υC1 (0− ) = Vs ,
υC2 (0) = υC2 (0− ) = Vs .
i2
R
C2
υC1
C1
υC2
i2
Ceq
R
(b) At t > 0
At t ≥ 0 (Fig. (b)):
According to Section 5-2.2, when two capacitors are in series, they add such that
Ceq =
C1C2
,
C1 +C2
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and their initial voltages add as well. In this case
υCeq (0) = υC2 (0) − υC1 (0) = Vs −Vs = 0.
Hence, no current will flow through the circuit:
i2 (t) = 0.
All rights reserved. Do not reproduce or distribute. © 2016 National Technology and Science Press