$($adapted from Prob. $8,$ p$.403,$ Brown's Introductory Physics II$)$ Consider the diagrams below. Switch $S$ has been closed for a very long time, such that the current in each part of the circuit has settled down to a constant value $($see left below$).$ At time $t=0,$ the switch is opened $($see right below$).$

$($a$)$ Before the switch is opened, what is the voltage across the inductor, and therefore how much does the inductor fight back against current flowing through its branch of the circuit?

$($b$)$ Given your answer to $($a$),$ determine the values of I,$I_1,$ and $I_2$ before the switch is opened, in terms of $V_0$ and $R.$

$($c$)$ Inductors are the circuit elements that ensure smooth and continuous changes in current, so the initial current through the inductor immediately after the switch is opened