For the circuit shown below, $=20vv,L=4\mathrm{.}0mH,$ and $R=5\mathrm{.}0.$ After steady state is reached with $S_1$ closed and $S_2$ open, $S_2$ is closed and immediately thereafter $($at $t=0)S_1$ is opened. Determine $($a$)$ the current through $L$ at $t=0,($b$)$ the current through $L$ at $t=4\mathrm{.}0{10}^{-4}s,$ and $($c$)$ the voltages across $L$ and $R_1$ at $t=4\mathrm{.}0{10}^{-4}$ s$.R_1=R_2=R.$