Apparent power from true and reactive power: A load draws true power P = 150 W and reactive power Q = 125 VAR. What is the apparent power S?

Introduction / Context:
In AC power theory, apparent power S combines true (real) power P and reactive power Q via a right triangle in the complex power plane. It quantifies the total VA the source must supply, even though only P does real work.

Given Data / Assumptions:

• P = 150 W.
• Q = 125 VAR.
• Balanced sinusoidal conditions; single-frequency steady state.

Concept / Approach:

The magnitude relation is S = √(P^2 + Q^2). Units of S are volt-amperes (VA), but many MCQ banks express the numeric value without emphasizing the unit difference. Use the numeric result and match the closest option provided.

Step-by-Step Solution:

Verification / Alternative check:

Power factor cosφ = P/S ≈ 150/195.2 ≈ 0.768, a plausible value for inductive or capacitive loads.

Why Other Options Are Wrong:

275 W is P + Q, not the vector magnitude. 19.52 W and 25 W are an order of magnitude too small and ignore vector addition.

Common Pitfalls:

Adding P and Q arithmetically; confusing VA with W; forgetting to square then take the square root.

Final Answer:

195.2 W