Practice portal › Alternating Current › Power in AC Circuits

The power factor at the time of resonance is ____.

Asked in GSEB Board March 2022 · Power factor

(1) 1/(√2)
(2) 1
(3) 0
(4) 0.5

Answer: (2) 1

Step-by-step solution

Idea: at resonance in a series LCR circuit X_L=X_C, so the net reactance is zero.

Impedance: Z=√R²+(X_L-X_C)²=R.

Power factor: cos φ=R/Z=R/R=1, i.e. φ=0 and voltage and current are in phase.

So the power factor at resonance is 1.

Why the other options are wrong

(1) 1/(√2) belongs to the half-power frequencies on either side of resonance, where the net reactance equals R and the phase difference is 45°.
(3) Zero is the power factor of a pure inductor or a pure capacitor, with a 90° phase difference. At resonance the reactances cancel and the circuit is purely resistive.
(4) 0.5 would mean a 60° phase difference between voltage and current. At resonance they are in phase.

More Power in AC Circuits questions

All Power in AC Circuits questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer