In the circuit of the figure below, the switch S has been open for a long time. It is then suddenly closed. Take $\mathcal{E} = 10.0 \text{ V}$, $R_1 = 48.0 \text{ k}\Omega$, $R_2 = 120 \text{ k}\Omega$, and $C = 12.0 \text{ \mu F}$.
(a) Determine the time constant before the switch is closed.
s
(b) Determine the time constant after the switch is closed.
s
(c) Let the switch be closed at $t = 0$. Determine the current in the switch as a function of time. (Assume $I$ is in A and $t$ is in s. Do not enter units in your expression. Use the following as necessary: $\mathcal{E}$, $R_1$, $R_2$, $C$)
$I = $
