For the circuit shown in Figure P4.41, assume that switches $S_1$ and $S_2$ have been held closed for a long time prior to $t=0 . S_1$ then opens at $t=0$; however, $S_2$ does not open until $t=48 \mathrm{~s}$. Also assume $R_1=5 \Omega, R_2=4 \Omega, R_3=3 \Omega, R_4=6 \Omega$, and $C_1=C_2=4 \mathrm{~F}$.
a. Find the capacitor voltage $v_C$ at $t=0$.
b. Find the time constant $\tau$ for $0<t<48 \mathrm{~s}$.
c. Find $v_C$ for $0<t<48 \mathrm{~s}$.
d. Find $\tau$ for $t>48 \mathrm{~s}$.
e. Find $v_C$ for $t>48 \mathrm{~s}$.
f. Sketch $v_C$ for all time.