Step 1:

Initially at , the switch is open and the inductor acts as short circuit.

Find the current in the circuit.

Substitute in the above equation.

Initially current flowing in the circuit is  A.

Step 2:

After , the switch is closed.

The resistances R and R are in parallel and the equivalent resistance is in series with inductor L.

The two resistance R and R are in parallel then

The voltage across each component is equal to the total circuit voltage.

This is first order linear differential equation.

Solution of first order linear differential equation is , where .

Solution of the differential equation : .

Substitute corresponding values.

Initial at the value of current is A.

Therefore substitute in equation (1).

Therefore current flowing in the circuit is  A.

Step 3:

Find the voltage across inductor L.

Voltage across inductor is .

Substitute in .

At ,

Volatge across inductor at is V.

Solution :

Volatge across inductor at is V.