In an electrical circuit ' R ', ' L ', ' C ' and an a.c. voltage source are all connected in series. When ' L ' is removed from the circuit, the phase difference between the voltage and the 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 ( 3 = 3 )

Step-by-step solution

Case analysis shows the circuit reaches resonance. When inductance L is removed, ₁ = 3 for the RC circuit gives 3 = X_C R , so X_C = 3 R . When capacitance C is removed, ₂ = 3 for the RL circuit gives 3 = X_L R , so X_L = 3 R . In the original RLC circuit, X_L = X_C , so the impedance simplifies to Z = R^2 + (X_L - X_C)^2 = R^2 = R . The power factor is therefore = R Z = 1 . Power factor: 1