An inductor of 10 mH, capacitor of 0.1 F and a resistor of 100 are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5 . The difference in the inductive reactance and capacitance reactance is 3 . The value of is _____.

Step-by-step solution

The power factor of an LCR series circuit is given by = R Z . Given = 0.5 and R = 100 . Substituting the values, we get: 0.5 = 100 Z Z = 200 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 : (200)^2 = (100)^2 + (X_L - X_C)^2 40000 = 10000 + (X_L - X_C)^2 (X_L - X_C)^2 = 30000 |X_L - X_C| = 100 3 The difference in inductive and capacitive reactance is given as 3 . Comparing the two expressions: 3 = 100 3 = 100 Answer: 100