3.2 TRANSIENTS IN CIRCUITS 129
i(t)
iR iC
S
I = 10 A vC(t)
t = 0
R = 2 Ω C^ = 5 F
−
+
(a)
Figure E3.2.2(a)RC circuit excited by
i(t)=I.(b)Capacitor voltagevC(t) =
20 ( 1 −e−t/^10 )V, fort>0.(c)Capacitor
currentiC(t)= 10 e−t/^10 A, fort>0.
0
12.64
20(1 − e−t/10)
vC(t), V
T = 10 2 T = 20
t, s
10
(b)
20.00
17.30
15.00
5.00
10.00
20
0
3.68
10 e−t/10
iC(t), A
T = 10
t, s
10
(c)
10
5
Just as the inductor current cannot change instantaneously, the capacitor voltage cannot change
instantaneously,
vC( 0 +)=vC( 0 −)
which happens to be zero in our case, as otherwise the capacitor currentiC=C(dvC/dt)would
become infinite. Thus we have
vC(t)=( 0 − 20 )e−t/^10 + 20 = 20
(
1 −e−t/^10
)
V, fort> 0
Then the capacitor current is obtained as
iC(t)=C
dvC
dt
= 10 e−t/^10 A, fort> 0