Electric circuit switch

Question

Answer 1

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 :

, where .

Find .

Comments

Contd..
Solution of the differential equation : .

Substitute the corresponding values.

Initially at , the current flowing in the circuit 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.