For the circuit shown in Eigure P4.41, assume that switches $S_1$ and $S_2$ have been held open for a long time prior to $t=0$ but then close at $t=0$. 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 $t>0$.
c. Find $v_C$ and sketch the function.
d. Evaluate the ratio $v_C$ to $v_C(\infty)$ at each of the following times: $t=0, \tau, 2 \tau$, $5 \tau, 10 \tau$.