For a series LCR circuit connected to an AC source, the parameters are R = 300 , C = 20 F , L = 1.0 henry , E _ rms = 50 V , and = 50/ Hz . Determine the average electric field energy stored in the capacitor and the average magnetic field energy stored in the coil.

Step-by-step solution

The angular frequency of the AC source is given by: = 2 = 2 50 = 100 rad/s The inductive reactance X_L is: X_L = L = 100 1.0 = 100 The capacitive reactance X_C is: X_C = 1 C = 1 100 20 10⁻⁶ = 500 The impedance Z of the series LCR circuit is: Z = R^2 + (X_C - X_L)^2 = 300^2 + (500 - 100)^2 = 300^2 + 400^2 = 500 The RMS current in the circuit is: I_ rms = E _ rms Z = 50 500 = 0.1 A The RMS voltage across the capacitor is: V_ C, rms = I_ rms X_C = 0.1 500 = 50 V The average electric field energy stored in the capacito