A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and voltage. The power factor of the circuit is:

Question

Accepted Answer

(2) 1.0. With L removed the circuit is RC, so tan π/3=(X_C)/R. With C removed it is RL, so tan π/3=(X_L)/R. Both give the same ratio, so X_L=X_C. In the full circuit those two reactances cancel exactly: the circuit is at resonance, Z=R, and the power factor is cos φ=R/Z=1. The point of the question is that each half tells you a reactance, and the two together tell you they are equal.

A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and voltage. The power factor of the circuit is:

Step-by-step solution

Why the other options are wrong