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A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor (√3/2) via a lossless line with a per-phase inductive reactance of 5 Ω. The per-phase synchronous reactance of the generator is 30 Ω with negligible armature resistance. If the generator is producing the rated current at the rated voltage, then the power factor at the terminal of the generator is

1. 0.63 lagging.
2. 0.87 lagging.
3. 0.63 leading.
4. 0.87 leading.

Correct answer: 0.87 lagging.

Solution

The correct option is right because the power factor at the terminal of the generator is determined by the relationship between the voltage, current, and the reactances involved. Given the inductive load and the reactance values, the resulting power factor is calculated to be 0.87 lagging, indicating that the load is drawing reactive power, which is typical for inductive loads.

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