Which expression correctly defines the apparent power S in a balanced three-phase system?

• A. √3 V_LL I cosφ
• B. 3 V_LL I
• C. √3 V_LL I sinφ
• D. √3 V_LL I

Answer: (D)

Apparent power is the product of voltage and current without regard to their phase angle. In a balanced three‑phase system, the line-to-line voltage is V_LL and the line current is I, and the three phase powers combine to give a total apparent power equal to √3 times V_LL times I. This comes from the relationships V_LL = √3 V_phase and summing the per‑phase contributions, which yields S = 3 V_phase I = 3 (V_LL/√3) I = √3 V_LL I.

The real power is P = S cosφ and the reactive power is Q = S sinφ, so:

• P = √3 V_LL I cosφ

• Q = √3 V_LL I sinφ

Thus the expression for apparent power does not include cosφ or sinφ and uses the √3 factor, making the correct form √3 V_LL I. The other expressions correspond to real power, reactive power, or a different scaling, not the magnitude of the complex power.