In LCR series circuit, when ' L ' is removed from the circuit, the phase difference between voltage and current in the circuit is 3 . If ' C ' is removed from the circuit instead of L then phase difference is again 3 . The power factor of the circuit is ( 60^ = 3 )

Step-by-step solution

Removing the inductor yields an RC series circuit with phase difference ₁ = 3 , where ₁ = X_C R . Given ( 3 ) = 3 , it follows that X_C R = 3 . Removing the capacitor yields an RL series circuit with phase difference ₂ = 3 , where ₂ = X_L R . Since ( 3 ) = 3 , we have X_L R = 3 . Combining these results gives X_C = 3 R and X_L = 3 R , implying X_L = X_C . For the original LCR circuit, the phase difference follows = X_L - X_C R . Substituting X_L - X_C = 0 yields = 0 , so = 0 . The power factor is = 0 = 1 .