What is the current when a circuit has a 1,500-watt load and a power factor of 86%, and operates from a three-phase 230-volt source?

What is the current when a circuit has a 1,500-watt load and a power factor of 86%, and operates from a three-phase 230-volt source?

• A. 9.7 amps
• B. 6.5 amps
• C. 4.4 amps
• D. 3.8 amps

Answer: (C)

In a balanced three-phase system, real power relates to the line current by P = √3 × V_LL × I × PF. Here, the real power is 1500 W, the line-to-line voltage is 230 V, and the power factor is 0.86. Solve for current: I = P / (√3 × V_LL × PF) = 1500 / (1.732 × 230 × 0.86) ≈ 1500 / 342.6 ≈ 4.38 A, which is about 4.4 A. The power factor effect means only a portion of the current is contributing to real power; higher PF (closer to 1) requires less current for the same real power. If you used a single-phase formula, you’d get a different value (and the standard three-phase approach with the √3 term matches the given 230 V source).

In a balanced three-phase system, real power relates to the line current by P = √3 × V_LL × I × PF. Here, the real power is 1500 W, the line-to-line voltage is 230 V, and the power factor is 0.86. Solve for current: I = P / (√3 × V_LL × PF) = 1500 / (1.732 × 230 × 0.86) ≈ 1500 / 342.6 ≈ 4.38 A, which is about 4.4 A.

The power factor effect means only a portion of the current is contributing to real power; higher PF (closer to 1) requires less current for the same real power. If you used a single-phase formula, you’d get a different value (and the standard three-phase approach with the √3 term matches the given 230 V source).