To find the inductor current in a switched circuit a long time after the switch is open.

A security alarm for an office building door is modeled by the circuit shown. The switch represents the door interlock, and V is the alarm indicator voltage. Find the current through the inductor, iL(t), for t>0. The switch has been closed for a long time at t=0.

This was actually a problem posted by one of the students and I provided the solution. This is just a detailed solution (step-by-step) to the same problem.