In a three-phase circuit with V_L = 480 V, I_L = 30 A, cosφ = 0.8, what is the real power P?

In a three-phase circuit with V_L = 480 V, I_L = 30 A, cosφ = 0.8, what is the real power P?

• A. 15.0 kW
• B. 19.9 kW
• C. 19.94 kW
• D. 25.8 kW

Answer: (C)

Real power in a three-phase circuit is the portion of the apparent power that does useful work. For a balanced system, P = √3 V_L I_L cosφ, where V_L is the line-to-line voltage, I_L is the line current, and cosφ is the power factor. With V_L = 480 V, I_L = 30 A, and cosφ = 0.8, P ≈ 1.732 × 480 × 30 × 0.8. First 480 × 30 = 14,400; times 0.8 gives 11,520; then 11,520 × 1.732 ≈ 19,953 W, or about 19.95 kW. This is essentially 19.94 kW, matching the given value.

Real power in a three-phase circuit is the portion of the apparent power that does useful work. For a balanced system, P = √3 V_L I_L cosφ, where V_L is the line-to-line voltage, I_L is the line current, and cosφ is the power factor. With V_L = 480 V, I_L = 30 A, and cosφ = 0.8, P ≈ 1.732 × 480 × 30 × 0.8. First 480 × 30 = 14,400; times 0.8 gives 11,520; then 11,520 × 1.732 ≈ 19,953 W, or about 19.95 kW. This is essentially 19.94 kW, matching the given value.