Electric switch circuit

Question

Answer 1

(1)

Step 1:

Initially at , the switch is closed and inductor is replaced by short circuit.

The resistance is short circuited.

Find the current in the circuit.

Initial current in the circuit : .

Substitute and in the above formula.

Initially current flowing in the circuit is .

Step 2:

After , the switch is open.

The resistance and are in series and is connected to inductor in series.

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

Substitute , , and .

This is first order linear differential equation.

Solution of first order linear differential equation :

, where .

Find .

Comments

Contd...

The differential equation is .

Solution of the differential equation : .

Substitute corresponding values.

Initially at , the current flowing in the circuit is .

Therefore substitute in equation (1).

Therefore current flowing in the circuit is .

Solution :

Current flowing in the circuit is .

Answer 2

(2)

Step 1:

Find the voltage across inductor .

Voltage across inductor is .

Substitute and in .

Voltage across inductor is  V.

Solution :

Voltage across inductor is  V.