LR, RC and LCR Circuits: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of LR, RC and LCR Circuits. Understanding the underlying formula is key to arriving at the correct answer below:

Since current lags voltage, \(tan(45^\circ) = \frac{X_L - X_C}{R} = 1 ⇒ X_L - X_C = R\). Substituting \(X_L = 2\pi f L\) and \(X_C = \frac{1}{2\pi f C}\), we get \(2\pi f L = R + \frac{1}{2\pi f C} = \frac{2\pi f C R + 1}{2\pi f C}\). Thus, \(L = \frac{2\pi f C R + 1}{4\pi^2 f^2 C}\).