Chapter 5, Problem 5.45HP

For the circuit shown in Figure P5.41, assume that switches $S_1$ and $S_2$ have been held closed for a longtime prior to $t=0$ . $S_1$ then opens at $t=0$ ; however, $S_2$ does not open until $t=48s$ . Also assume $R_1=5\Omega ,R_2=4\Omega ,R_3=3\Omega ,R_4=6\Omega ,$ and $C_1=C_2=4F$.
a Find the capacitor voltage $v_c$ at $t=0$ .
b. Find the time constant $\tau$ for $0<t<48s$ .
c. Find $v_c$ for $0<t<48s$ .
d. Find $\tau$ for $t<48s$ .
e. Find $v_c$ for $t<48s$ .
f. Sketch $v_c$ for all time.