Which formulas correctly define P, Q, S, and PF for an AC circuit?

• A. P = VI; Q = VI; S = VI; PF = P / S
• B. P = VI cos φ; Q = VI sin φ; S = VI; PF = P / S = cos φ
• C. P = V^2 / R; Q = V^2 / X; S = V^2 / Z; PF = Q / P
• D. P = I^2 R; Q = I^2 X; S = V I; PF = S / P

Answer: (B)

In sinusoidal AC circuits, the different powers are tied to how much the current lags or leads the voltage. Active power, the real work done, is P = V I cos φ, where φ is the phase angle between voltage and current. Reactive power, which is alternately stored and released by the reactive elements, is Q = V I sin φ. The apparent power is the combined effect in magnitude, S = V I (the product of RMS voltage and current, representing the total power flow). The power factor, showing how effectively the circuit uses power, is PF = P / S, which simplifies to PF = cos φ.

That’s why the correct set of formulas is P = VI cos φ, Q = VI sin φ, S = VI, PF = P / S = cos φ. The other options mix up these relationships or use an incorrect PF expression, for example by treating Q as VI in all cases or by swapping the PF relationship.