Solution 2.9.6.3 R i(t) Switch closes at t = 0 e(t) C v C (0) Figure 1: Series RC circuit For the circuit of Figure 1, weassume v c (0) = 0. Kircho 's law yields e(t)= 1 C Z t 0 i()d + v c (0)+ i(t)R: Applying the Laplace transform weobtain E(s) = 1 Cs I(s)+ v c (0) s + I(s)R This can be rearranged as I(s)= 1 R  sE(s);v c (0) s +1=RC  For e(t)=V;; E(s)=V=s: Then for v c (0)=0,wehave I(s)= 1 R  V s +1=RC  ;; and i(t)=(1=R)e ;t=RC 1(t): 1