Which expression correctly represents the input power for a balanced three-phase system using line voltage V_L, line current I, and power factor PF?

• A. P = V_L I PF
• B. P = 3 V_L I PF
• C. P = V_L I / PF
• D. P = sqrt(3) V_L I PF

Answer: (D)

In a balanced three-phase system, the real input power equals the three-phase apparent power times the power factor. The three-phase apparent power is S = √3 V_L I, where V_L is the line voltage and I is the line current. Since PF = cosφ, the real power is P = S PF = (√3 V_L I) PF = √3 V_L I PF. This is why the correct expression uses the √3 factor with V_L, I, and PF.

The other forms don’t fit because they either omit the √3 factor needed for line quantities in a three-phase system, or they mix up the relationship between apparent power and real power (e.g., dividing by PF or multiplying by 3 in this context).