A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains resistance of 100 , capacitor of capacitive reactance X_C and inductor of inductive reactance X_L = 150 . If the power factor of the circuit is 8 10 and, X_L > X_C , then the value of X_C is

Step-by-step solution

The power factor of a series LCR circuit is given by = R Z . Substituting the given values: 8 10 = 100 Z Z = 100 10 8 = 125 The impedance Z of the circuit is also given by: Z = R^2 + (X_L - X_C)^2 Squaring both sides and substituting the values of Z and R : (125)^2 = (100)^2 + (X_L - X_C)^2 15625 = 10000 + (X_L - X_C)^2 (X_L - X_C)^2 = 5625 Taking the square root on both sides: X_L - X_C = 75 Since it is given that X_L > X_C , we take the positive value: X_L - X_C = 75 Substituting X_L = 150 : 150 - X_C = 75 X_C =