An AC source of 200 V (rms) is connected across a series LCR circuit. The rms current in the circuit is observed to be 4 A , and the voltage leads the current by a phase angle of 53^ . If the capacitive reactance of the circuit is 10 , what are the values of the resistance and the inductive reactance, respectively? (Take 53^ = 3 5 )

Step-by-step solution

The impedance of the circuit is given by: Z = V_ rms I_ rms = 200 4 = 50 From the impedance triangle, the resistance R is: R = Z = 50 53^ = 50 3 5 = 30 Since the voltage leads the current, the circuit is inductive ( X_L > X_C ). The net reactance is: X_L - X_C = Z = 50 53^ = 50 4 5 = 40 Given that the capacitive reactance X_C = 10 : X_L - 10 = 40 X_L = 50 Thus, the resistance is 30 and the inductive reactance is 50 . Answer: 30 and 50