Electric circuit switch

Question

Answer 1

(1)

Step 1:

Case (I) :

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

The resistance and the resistance are in series.

Find the current in the circuit.

Substitute , and in the above formula.

Initially current flowing in the circuit is .

Step 2:

Case (II) :

After , the switch is closed.

The resistor is short circuited.

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 differential equation.

This is first order linear differential equation.

Solution of first order linear differential equation :

, where .

Find .

Comments

Contd...

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 A.

Solution :

Current flowing in the circuit is A.

Answer 2

(2)

Step 1:

Find the voltage across inductor .

Voltage across inductor is .

Substitute and A in .

Solution :

Voltage across inductor is  V.