Question

Problem 1 Find the voltage v) and I() by means of Laplace transform. (35 pts) I H 10m) V 0.5F T Note the source is a voltage source (not current source)

Answer 1

"Requirement is V_0 (t) and I_L (t) u (t) = unit step function and it defines u (t) = {1: t > 0 0: t < 0 taking s - domain then new circuit will becomes using K C L at node ""v"" 10/s - v/1 = v/2/s + v/s + 1/s rightarrow 10/s - v = v s/2 + v s/s^2 + 1 \r\n rightarrow 10/s - v = v s/2 + v s/s^2 + 1 rightarrow 10/s = v s/2 + v + v s/s^2 + 1 = v [s/2 + 1 + s/s^2 + 1] = v [s (s^2 + 1) + 2 (s^2 +"