If kilowatts are known, which expression gives current in a three-phase system?

• A. I = KW × 1000 / Volts × PF × 1.73
• B. I = KW × 1000 / (Volts × PF × 1.73)
• C. I = KW × 1000 / Volts × PF × 1.73
• D. I = KW × 1000 / Volts ÷ (PF × 1.73)

Answer: (C)

In a three-phase system, real power relates to current by P = √3 × V_L × I × PF. To find the current when given power in kilowatts, convert P to watts (P = KW × 1000) and solve for current: I = P / (√3 × V_L × PF). This becomes I = KW × 1000 / (Volts × PF × 1.73), using 1.73 as an approximation for √3. The denominator must include Volts, PF, and the √3 factor because each plays a role in determining how much current is needed to deliver the real power: voltage provides the driving potential, PF accounts for how much of that power is actually doing useful work, and √3 arises from the relationship between line voltage and line current in a three-phase system. For example, with 100 kW, 480 V, and PF of 0.9, I ≈ 1000000 / (480 × 0.9 × 1.73) ≈ 134 A.