What is the power factor of a purely resistive AC circuit?
It is equal to 1
Power factor in an AC circuit is defined as the cosine of the phase angle between the supply voltage and the resulting current, written as \(\cos\phi\).
This angle exists because reactive elements, inductance or capacitance, make the current lead or lag the voltage; a pure resistance has no such reactance.
In a purely resistive circuit the current rises and falls exactly in step with the voltage, so they reach their peaks together and the phase angle is \(\phi=0^\circ\).
Substituting this angle gives the power factor as \(\cos 0^\circ = 1\), that is unity.
A unity power factor means all the supplied volt-amperes are converted into useful real power, with no reactive component circulating.
The value cannot be less than 1 (that needs some reactance), cannot be 0 (that would need a pure reactance with no resistance), and can never exceed 1 because the cosine of any angle has a maximum of 1.
Hence, the answer is It is equal to 1.
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