Circuit R,C, switch

Question

Answer 1

Step 1:

At , the switch is closed and capacitor acts as a open circuit.

The resistance is short circuited.

The resistor and are in series.

The current flowing in the circuit is .

Substitute , and .

Therefore current flowing in the circuit is .

Step 2:

At , the switch is open and capacitor starts discharging.

Apply KVL for the first loop.

Apply KVL for the second loop.

Apply Laplace transform to the equation (1).

Laplace transform of constant .

Laplace transform of integral function .

Comments

Contd...

Apply Laplace transform to the equation (2).

Substitute in equation (3).

Apply inverse laplace transform.

Inverse Laplace transform :.

.

Since the current direction is in opposite direction, .

Current across the capacitor is .

Solution :

Current across the capacitor is .