What is the power factor of an ac circuit?

The correct answer is Option (1) → The ratio of the average power to the product of the rms voltage and the rms current (\( \cos\phi \))

The average power dissipated in an ac circuit is \( P=VI\cos\phi \). Here \( V \) and \( I \) are rms values, and \( \phi \) is the phase angle between the voltage and the current.

Option (1) The ratio of the average power to the product of the rms voltage and the rms current (\( \cos\phi \)) — Correct. From \( P=VI\cos\phi \), the factor \( \cos\phi=P/VI \) is the power factor. It is a pure number between 0 and 1. It is 1 for a purely resistive circuit and 0 for a purely inductive or capacitive one.

Option (2) The power of the ac — Incorrect. Power is measured in watts, but the power factor \( \cos\phi \) has no unit. It only tells what fraction of \( VI \) is actually dissipated.

Option (3) The mean power of the circuit — Incorrect. The mean power is \( VI\cos\phi \), in watts. The power factor is only the factor \( \cos\phi \) in it.

NCERT (2026-27):
Power in AC Circuit: The Power Factor – “The average power over a cycle is given by the average of the two terms … Therefore,”

    \( \displaystyle P=\frac{v_mi_m}{2}\cos\phi=\frac{v_m}{\sqrt{2}}\frac{i_m}{\sqrt{2}}\cos\phi=VI\cos\phi \qquad [7.30(a)] \)

“… So, the average power dissipated depends not only on the voltage and current but also on the cosine of the phase angle φ between them. The quantity cosφ is called the power factor.”