Alternating Current: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Alternating Current. Understanding the underlying formula is key to arriving at the correct answer below:

Current leads voltage by $45^\circ$, so capacitive reactance is greater than inductive reactance.
$\tan \phi = \frac{X_C - X_L}{R} \implies \tan 45^\circ = \frac{X_C - X_L}{R} \implies 1 = \frac{X_C - X_L}{R}$.
$X_C = X_L + R \implies \frac{1}{2\pi f C} = 2\pi f L + R$.
Therefore, $C = \frac{1}{2\pi f(2\pi f L + R)}$.