What is power factor and how is it calculated in AC circuits?

• A. PF = cos(phi) = Real power / Apparent power
• B. PF = Real power / Voltage
• C. PF = Apparent power / Real power
• D. PF = Reactive power / Apparent power

Answer: (C)

Power factor tells you how effectively the current is being converted into useful work. It’s the cosine of the phase angle between voltage and current, phi. In an AC circuit, real power P (watts) is the actual energy used, while apparent power S (volt-amperes) is the product of RMS voltage and RMS current. The reactive power Q (volt-amps reactive) accounts for energy alternately stored and released by inductors or capacitors.

Because S^2 = P^2 + Q^2, the ratio P/S gives the fraction of power doing useful work. That ratio is the power factor, and it’s also equal to cos(phi). So the correct description is: power factor equals cos(phi), which equals real power divided by apparent power. A high power factor (close to 1) means most power is used for work; a low power factor indicates more energy is wasted as reactive power. When the load is purely resistive, phi is zero and the power factor is 1. Inductive loads cause lagging current (phi > 0) and capacitive loads cause leading current (phi < 0), but in all cases the magnitude of the power factor is P/S.