A series LCR circuit is connected to an a.c. source of 230 ~V , 50 ~Hz . The circuit contains resistance of 80 an inductor having inductive reactance 70 and a capacitor of capacitive reactance 130 . The power factor of the circuit is x . The value of x is

Step-by-step solution

The power factor of a series LCR circuit is determined by the ratio of resistance to impedance. Given resistance R = 80 , inductive reactance X_L = 70 , and capacitive reactance X_C = 130 , the net reactance is X = X_C - X_L = 60 since X_C > X_L . The impedance follows as Z = R^2 + X^2 = 80^2 + 60^2 = 10000 = 100 . Thus, the power factor is = R/Z = 80/100 = 0.8 . This corresponds to option B , so the answer is B .