Which formula best expresses the input real power for a balanced three-phase motor given line voltage, line current, and power factor?

• A. sqrt(3) × V_line × I_line × PF
• B. V_line × I_line × PF
• C. 3 × V_line × I_line × PF
• D. V_line × I_line / PF

Answer: (A)

For a balanced three-phase system, input real power is found by multiplying the three-phase apparent power by the power factor. The three-phase apparent power is S = √3 × V_line × I_line, so the real power is P = √3 × V_line × I_line × PF. This also ties to P = 3 × V_phase × I_phase × PF, since V_line = √3 × V_phase and I_line = I_phase in a balanced setup, leading to the same result.

The other forms don’t reflect this three-phase relationship: using just V_line × I_line × PF treats it as a single-phase power, the 3 × V_line × I_line × PF multiplies by an extra √3, and V_line × I_line / PF would give an incorrect result since real power is S × PF, not S divided by PF.