Electric switch circuit

Question

Answer 1

(1)

Step 1:

The resistance and the capacitor are in series.

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

Solve the equation for current i.

Substitute , and in .

Apply Laplace transform to find current i.

Laplace transform of constant .

Laplace transform of integral function .

The initial voltage of the capacitor when is .

Apply inverse Laplace transform.

Inverse Laplace transform :.

Solution :

The current flowing through the circuit at any moment of time is .

Answer 2

(2)

Step 1:

Find the voltage across resistor .

Volatge across resistor is .

Substitute and in .

Solution :

Volatge across resistor is .

Answer 3

(3)

Step 1:

Find the voltage across capacitor .

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

So the volatge across capacitor is .

From (2) .

Solution :

Volatge across capacitor is .