In a balanced three-phase system, what is the expression for the total apparent power S using line voltage and line current?

• A. S = √3 V_LL I_L
• B. S = 3 V_LL I_L
• C. S = V_LL I_L
• D. S = √3 V_LN I_L

Answer: (A)

In a balanced three-phase system, the total apparent power comes from adding the per-phase powers: S = 3 V_phase I_phase. Since V_LL = √3 V_phase and the line current equals the phase current for a balanced setup, substituting gives S = √3 V_LL I_L. This relation holds whether the system is wye or delta, because the √3 factor accounts for the relationship between line and phase quantities in three-phase power. The other forms miss the √3 or mix line-to-neutral voltage with line current, which does not represent the total three-phase apparent power with line quantities in a balanced system.