In a balanced three-phase system, how is real power P related to apparent power S and power factor PF?

• A. P = S × PF
• B. P = S / PF
• C. P = √(S^2 − PF^2)
• D. P = PF × S^2

Answer: (A)

In an AC system, real power is the portion of the apparent power that actually does useful work, while apparent power is the product of voltage and current regardless of phase. The power factor tells you how much of that apparent power is being converted to real work, and it is defined as PF = P / S. So the real power is P = S × PF. In a balanced three-phase setup, S = √3 V_L I_L and P = √3 V_L I_L cos φ with PF = cos φ, which leads to P = S cos φ = S × PF. This is the straightforward relationship that ties together real power, apparent power, and power factor.