Page 92 - LAPLACE TRANSFORM

SOLUTION

By using Kirchhoff’s voltage law;

VL + VC = VS

di
1
t
-3t
L + ∫ i(t)dt = 12e
dt C 0

By applying the Laplace transformation method;

1 12
L [sI(s) − i(0)] + [I(s) + q0] =
CS s+3

By assuming zero initial condition;

1 12
L [sI(s)] + [ I(s)] =
CS s + 3

I(s) 12
4sI(s) + =
50mS s + 3
20I(s) 12
4sI(s) + =
s + 3

12
I(s)[ 4s + ] =
s + 3
2
4s + 20 12
I(s) { } =
s s + 3
2
4s + 20 12 s
I(s) { } = x
2
s s + 3 (4s + 20)

I(s) = 12s = 12s = 3s
2
2
2
(s + 3)(4s + 20) (s + 3) .4(s + 5) (s + 3)(s + 5)
I(s) = 3s = A + (Bs+C)
2
2
(s + 3)(s + 5) (s + 3) (s + 5)

2
multiply each side with ( + 3)( + 5)

3s = A( + ) + (Bs + C) (s + 3)

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