$(25$ points$)$ In the circuit shown below, the switch $S$ is closed at $t=0.$

$($a$)$ What is the current through each resistor just after the switch is closed?

$($b$)$ What is the rate of current change across each inductor just after the switch is closed?

$($c$)$ What is the current through each resistor after a very long time?

$($d$)$ What is the charge stored in each capacitor after a very long time?

$($Answer all only in terms of V$,$ R$,C$ and $L$ given in the circuit.$)$