$[2/3$ Points$]$

SERPSE$1027\mathrm{.}4.$P$\mathrm{.}026.$

In the circuit of the figure below, the switch $S$ has been open for a long time. It is then suddenly closed. $($Use the following as necessary: $E$ for ${}_2,R_1,R_2,t,$ and $C.)$

$($a$)$ Determine the time constant before the switch is closed.

$=$

$($b$)$ Determine the time constant after the switch is closed.

$=$

$($c$)$ Let the switch be closed at $t=0.$ Determine the current in the switch as a function of time.

$I=$

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