In a three-phase circuit with VL = 400 V, IL = 20 A, and PF = 0.85, calculate real power.

In a three-phase circuit with VL = 400 V, IL = 20 A, and PF = 0.85, calculate real power.

• A. 10.0 kW
• B. 11.8 kW
• C. 15.0 kW
• D. 20.0 kW

Answer: (B)

Real power in a balanced three-phase system comes from the portion of the apparent power carried in phase alignment, captured by P = √3 × V_L × I_L × PF. Here the line voltage is 400 V, the line current is 20 A, and the power factor is 0.85, so the calculation is P = √3 × 400 × 20 × 0.85. Using √3 ≈ 1.732, this becomes P ≈ 1.732 × 400 × 20 × 0.85 = 11,777.6 W, about 11.8 kW. For context, the apparent power is S = √3 × 400 × 20 ≈ 13.856 kVA, and real power is S × PF ≈ 13.856 kVA × 0.85 ≈ 11.8 kW.

Real power in a balanced three-phase system comes from the portion of the apparent power carried in phase alignment, captured by P = √3 × V_L × I_L × PF. Here the line voltage is 400 V, the line current is 20 A, and the power factor is 0.85, so the calculation is P = √3 × 400 × 20 × 0.85.

Using √3 ≈ 1.732, this becomes P ≈ 1.732 × 400 × 20 × 0.85 = 11,777.6 W, about 11.8 kW.

For context, the apparent power is S = √3 × 400 × 20 ≈ 13.856 kVA, and real power is S × PF ≈ 13.856 kVA × 0.85 ≈ 11.8 kW.