Circuit R,L, and switch

Question

Answer 1

(1)

Step 1:

Case (I) :

Initially at , the switch is open 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:

Case (II) :

After , the switch is closed.

The resistance and are in parallel.

.

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

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

Substitute , , and .

This is first order linear differential equation.

Comments

Contd...

Solution of first order linear differential equation :

, where .

Find .

Solution of the differential equation : .

Substitute corresponding values.

Initially at , the value of current is .

Therefore substitute in equation (1).

Therefore, current flowing in the circuit is  A.

Current flowing across the series network is same, hence current flowing across the inductor is  A.

Solution :

Current flowing across the inductor is  A.

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.