An inductor of reactance 100 , a capacitor of reactance 50 , and a resistor of resistance 50 are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is ____

Step-by-step solution

Given X_L = 100 , X_C = 50 , and R = 50 . The impedance of the series LCR circuit is given by: Z = R^2 + (X_L - X_C)^2 Z = 50^2 + (100 - 50)^2 = 50^2 + 50^2 = 50 2 The RMS current in the circuit is: I_ rms = V_ rms Z = 10 50 2 = 1 5 2 A The average power dissipated in the circuit is: P_ avg = I_ rms ^2 R P_ avg = ( 1 5 2 )^2 50 = 1 50 50 = 1 W Answer: 1 W