$4.(25$ points$)$ In the circuit shown below, the switch $\backslash ($ S $\backslash )$ is closed at $\backslash ($ t$=0\backslash ).$

$($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 $\backslash (\backslash$mathrm$\{$V$\},$ R$,$ C $\backslash )$ and $\backslash ($ L $\backslash )$ given in the circuit.$)$