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

Sol: As current leads the voltage by 45°

$\large tan\phi = \frac{X_C – X_L}{R}$

$\large tan45^o = \frac{X_C – X_L}{R}$

$\large 1 = \frac{X_C – X_L}{R}$

$\large X_C – X_L = R $

$\large X_C = X_L + R $

$\large \frac{1}{\omega C} = \omega L + R $

$\large C = \frac{1}{\omega (\omega L + R)}$

$\large C = \frac{1}{2\pi f (2\pi f L + R)}$