Problem: RL Circuits $(10$ pts$.)$

Consider the RL circuit shown in the diagram. When studying RL circuits, it helps to remember the behavior of inductors at two times:

$1.$ Right after any change is made in the circuit, an inductor will maintain the same current that was flowing through it before the change.

$2.$ After a long time, an inductor behaves like a wire.

A$.(3$ pts$.)$ Find the three currents $\backslash ($ I$\_\{1\},$ I$\_\{2\}\backslash ),$ and $\backslash ($ I$\_\{3\}\backslash )$ right after the switch is first closed.

B$.(3$ pts$.)$ Find the three currents $\backslash ($ I$\_\{1\},$ I$\_\{2\}\backslash ),$ and $\backslash ($ I$\_\{3\}\backslash )$ after the currents have reached steady$-$state values.

C$.(3$ pts$.)$ Find the three currents $\backslash ($ I$\_\{1\},$ I$\_\{2\}\backslash ),$ and $\backslash ($ I$\_\{3\}\backslash )$ at the instant the switch is reopened after being closed for a long time.

D$.(1$ pt$.)$ What is the emf across the inductor the instant the switch is opened in part $($C$)?$