In an electrical circuit R, L, C and AC 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

Step-by-step solution

In an LCR series circuit, the phase difference is given by = X_L - X_C R . When L is removed, the circuit contains only R and C . The phase difference is ₁ = - / 3 . Thus, (- / 3) = -X_C R , which implies X_C R = 3 , so X_C = R 3 . When C is removed, the circuit contains only R and L . The phase difference is ₂ = / 3 . Thus, ( / 3) = X_L R , which implies X_L R = 3 , so X_L = R 3 . In the original LCR series circuit, the net reactance is X = X_L - X_C = R 3 - R 3 = 0 . The circuit is in resonance, so the phase diff