The resistor ' R ' inductance ' L ' and capacitance ' C ' are connected in series with an a.c. source. When 'L' is removed from the circuit, the phase difference between voltage and current in the circuit is 3 . If instead, C is removed from the circuit, the phase difference is again 3 . The power factor of the circuit is

Step-by-step solution

When L is removed, the circuit becomes an RC circuit. The phase difference is = 3 . = X_C R ( 3 ) = X_C R X_C = R 3 When C is removed, the circuit becomes an RL circuit. The phase difference is again = 3 . = X_L R ( 3 ) = X_L R X_L = R 3 In the series RLC circuit, the net reactance is X = X_L - X_C . Since X_L = X_C = R 3 , we have X = 0 . The impedance of the circuit is Z = R^2 + (X_L - X_C)^2 = R . The power factor of the circuit is = R Z = R R = 1 . Answer: 1