An AC voltage V = 100 2 (100 t) Volts is applied to a series LCR circuit with R = 40 , , L = 0.7 H, and C = 250 , F. The average power dissipated in the circuit is :

Step-by-step solution

From the voltage equation V = 100 2 (100 t) , the peak voltage is V_m = 100 2 V and the angular frequency is = 100 rad/s. The RMS voltage is V_ rms = V_m 2 = 100 2 2 = 100 V. The inductive reactance is X_L = L = 100 0.7 = 70 , . The capacitive reactance is X_C = 1 C = 1 100 250 10⁻⁶ = 1 25 10⁻³ = 40 , . The impedance of the circuit is Z = R^2 + (X_L - X_C)^2 = 40^2 + (70 - 40)^2 = 40^2 + 30^2 = 50 , . The RMS current in the circuit is I_ rms = V_ rms Z = 100 50 = 2 A. The average power dissipated is P = I_ rms ^2 R