Problem #$3$ : $43$ pts

Initially switch $S_1$ is closed and $S_2$ is open so that inductor $L,$ resistor $R$ and ideal battery $V$ are connected in series.

A$.$ Find the current through $R$ when switch $S_1$ has been closed for a very long time.

B$.$ Find the energy stored in $L$ when switch $S_1$ has been closed for a very long time.

At time $t=0$ switch $S_1$ opens and switch $S_2$ closes.

C$.$ Find the magnitude of the current $I_R$ through the resistor $R$ at time $t=0.$

D$.$ Is the current $I_R$ flowing to the right or left at time $t=0?$

E$.$ Find the magnitude of $d\frac{l_R}{d}t$ at time $t=0.$

F$.$ Find the current $I_R$ in the resistor $R$ at time $t=2\mathrm{.}0$ seconds.