An AC source is connected to a series RC circuit where R = 300 , C = 25 F , E ₀ = 50 V , and = 50/ Hz . Determine the peak current and the average power dissipated in the circuit.

Step-by-step solution

Angular frequency = 2 = 2 50 = 100 rad/s Capacitive reactance X_C = 1 C = 1 100 25 10⁻⁶ = 400 Impedance of the circuit Z = R^2 + X_C^2 = 300^2 + 400^2 = 500 Peak current I₀ = E ₀ Z = 50 500 = 0.10 A Average power dissipated P_ avg = I_ rms ^2 R = ( I₀ 2 )^2 R P_ avg = (0.10)^2 2 300 = 1.5 W