0195136047.pdf

186 TIME-DEPENDENT CIRCUIT ANALYSIS

(b) 3

d^2 i

dt^2

+ 7

di

dt

+ 2 i=10cos2t;i

(

0 +

)

=4A;

di

( dt

0 +

)

=−4A/s

(c)

d^2 i

dt^2

+ 2

di

dt

+ 2 i =sint−e−^2 t;i

(

0 +

)

=

0 ;

di

dt

(

0 +

)

=4A/s

Identify the forced and natural response compo-

nents in each case.

3.3.6Determine the Laplace transform of the waveform

shown in Figure P3.3.6.

3.3.7In the circuit shown in Figure P3.3.7, the switchS

has been open for a long time. Att=0, the switch

is closed. Find the currentsi 1 (t) andi 2 (t) fort≥ 0

with the use of the Laplace transform method.

*3.3.8Determinev(t) andiL(t)in the circuit shown in

Figure P3.3.8, given thati(t)= 10 te−tu(t).

3.3.9The switchSin the circuit of Figure P3.3.9 has

been open for a long time before it is closed at

t=0. DeterminevL(t)fort≥0.

3.3.10Determinev(t) in the circuit of Figure P3.3.10 if

i(t) is a pulse of amplitude 100μA and duration

10 μs.

f(t)

t, seconds

1 2

10

− 10

Figure P3.3.6

S

t = 0

8 Ω

4 Ω

2 Ω

100 V

+

−

i i^2 (t)

1 (t)

2 H

1 H Figure P3.3.7

10 Ω 9 iL(t)

+

−

i(t)

iL(t)

v(t) 1 H

Figure P3.3.8

10 V

S

t = 0

0.05 F

+^5 Ω

−

+

−

2 H vL(t)

Figure P3.3.9