Question

In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by 45°. The value of C is ______.

Options

• `1/(πf(2πfL - R))`

• `1/(2πf(2πfL - R))`

• `1/(πf(2πfL + R))`

• `1/(2πf(2πfL + R))`

Answer 1

In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by 45°. The value of C is `1/(2πf(2πfL + R))`.

Explanation:

Let, Inductance = L

Conductance = C

Resistance = R

Frequency = f

Phase Difference between current and voltage = 

∴ `tan phi = (X_L - X_C)/R`    ...(1)

The current leads the voltage by 45°

Therefore, `phi` = 45°

`tan phi` = tan 45° =  1      ...(2)

Put the values in equation (1) and (2) and calculate:

∴ `(X_L - X_C)/R = -1`

`X_L - X_C = - R`

`X_C = X_L + R`

`1/(2pifC) = 2pifL + R`

C = `1/(2pif(2pifL + R))`