An LCR series circuit driven with E_ rms = 90 V at frequency f_d = 30 Hz has resistance R = 80 , , an inductance with inductive reactance X_L = 20.0 , and capacitance with capacitive reactance X_C = 80.0 , . The power factor of the circuit is _______.

Step-by-step solution

The impedance of the LCR series circuit is given by Z = R^2 + (X_C - X_L)^2 . Substituting the given values: Z = 80^2 + (80 - 20)^2 Z = 80^2 + 60^2 Z = 6400 + 3600 = 10000 = 100 , The power factor of the circuit is given by = R Z . = 80 100 = 0.8 Answer: 0.8