A series LCR circuit is connected to an a.c. source of 220 V, 50 Hz. The circuit contains a resistance R = 80 , , an inductor of inductive reactance 70 , and capacitor of capacitive reactance 130 , . The power factor of the circuit is x 10 . The value of x is

Step-by-step solution

The impedance of the series LCR circuit is given by Z = R^2 + (X_C - X_L)^2 Substituting the given values: Z = 80^2 + (130 - 70)^2 Z = 80^2 + 60^2 Z = 6400 + 3600 = 10000 = 100 , The power factor of the circuit is = R Z = 80 100 = 8 10 Comparing this with x 10 , we get x = 8 . Answer: 8