For the following circuit: Find the Laplace current, l(s). Is the current steady
ID: 1934462 • Letter: F
Question
For the following circuit: Find the Laplace current, l(s). Is the current steady-state and/or transient?Explanation / Answer
In laplace domain, R -----> R L -----> sL C -----> 1/sC u(t) ----> 1/s a) I(s) = Vin(s)/ ( R + sL + 1/sC) I(s) = (1/s)/(18 + 2s + 40/s) I(s) = (1/2)/(s^2 + 9s + 20) b) Rewriting I(s) as I(s) = (1/2)/( (s + 9/2)^2 - (1/2)^2 ) using, sinh(at)u(t) -----> a/(s^2 - a^2) and x(t)e^at -----> X(s-a) we have, i(t) = e^(-4.5t)*sinh(0.5t)u(t) c) The current obtained by inverse laplace tranform is always the transient current ( Steady state value is given by lim s->o {sI(s)} )