Which expression correctly defines apparent power S in terms of P and Q?

• A. S = P + Q
• B. S = P^2 + Q^2
• C. S = √(P^2 + Q^2)
• D. S = √(P^2 - Q^2)

Answer: (C)

Apparent power is the magnitude of the complex power, which combines real power P and reactive power Q as perpendicular components. In AC power, complex power is written as S = P + jQ, so the overall size of this power vector is its length in the P–Q plane. That length is found by the Pythagorean relation, giving S = sqrt(P^2 + Q^2). This expresses how P and Q together determine the total apparent power stored or delivered, with S measured in volt-amperes (VA). Since P and Q are perpendicular components of power, you can’t just add them directly, and you don’t take the square root of their difference—that wouldn’t reflect the true geometric combination of the two orthogonal parts.