Step 1:

Initially at , the inductor acts as closed circuit.

The resistance is  .

Find the current in the circuit.

Substitute and in the above formula.

Initially current flowing in the circuit is .

Step 2:

After , the voltage is increased by 2 V.

The input voltage is 12 V.

The resistance and the inductor are in series.

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

Substitute and in the above.

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 .

Therefore substitute in equation (1).

Therefore current flowing in the circuit is .

Solution :

Current flowing in the circuit is .

Step 1:

Find the voltage across inductor .

Volatge across resistor is .

Substitute and in .

Solution :

Volatge across resistor is .

Step 1:

Find the voltage across inductor .

Volatge across inductor is .

Substitute and in .

Volatge across inductor is  V.

Solution :

Volatge across inductor is  V.