What is the standard formula for real power in a balanced three-phase circuit?

• A. P = √3 × VL × IL × PF
• B. P = 3 × VL × IL × PF
• C. P = VL × IL
• D. P = √3 × VL × PF

Answer: (A)

Real power in a balanced three-phase system comes from the sum of the real power in each phase, which is V_Ph × I_Ph × PF for one phase. With three identical phases, that total is 3 × V_Ph × I_Ph × PF. This can be rewritten using line quantities: the line-to-line voltage is V_LL = √3 × V_Ph, and the line current I_L is related to the phase current depending on the connection, but for a balanced system the standard form that uses practical, readily measured values is P = √3 × V_LL × I_L × PF.

This shows why the line values are used in the formula: you multiply the line-to-line voltage by the line current and the power factor to get real power for the whole three-phase system. If the power factor is 1, you simply have P = √3 × V_LL × I_L. You can also express the same quantity as P = 3 × V_Ph × I_Ph × PF, which is mathematically equivalent when using the appropriate phase voltages and currents.