RL circut

Question

Answer 1

(1)

Step 1:

Initially at , the inductor acts as short 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 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 the corresponding values.

Initially at , the current 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 resistor .

Voltage across resistor is .

Substitute and in .

Voltage across resistor is  V.

Solution :

Voltage across resistor is  V.

Answer 3

(3)

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.