0195136047.pdf

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