RC 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 the above equation.

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 : .

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

Solution :

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

Answer 2

(2)

Step 1:

Find the voltage across capacitor .

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

So the voltage across capacitor is .

Find voltage across resistor : .

Substitute and .

Now substitute and in .

Voltage across capacitor is  V.

Solution :

Voltage across capacitor is V.