Page 99 - LAPLACE TRANSFORM

Example 8 (RLC Series circuit)

By using Laplace transform, solve for the current i(t) if the S1 switch is closed and

calculate i(t) when t=2s. Assume that t=0, i0 =0 and q0=0.

SOLUTION

VR + VL + VC = VS

di 1 t
Ri(t) + L + ∫ i(t)dt = Vs
dt C 0

By applying the Laplace transform method;

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

I(s) Vs
R I(s) + L sI(s) + =
C
I(s) 25
4I(s) + (1)sI(s) + =

I(s) 25
4I(s) + sI(s) + =

20 25
I(s) { 4 + s + } =
s
2
4 + + 20 25
I(s) { } =
s

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