For a three-phase generator operating at full load and producing 186.84 kW, what is the full load current if the power factor is 75%?

To determine the full load current for a three-phase generator producing 186.84 kW at a power factor of 75%, it's essential to understand the formula for calculating power in a three-phase system.

The formula for three-phase power (P) involves the current (I), voltage (V), the square root of 3 (√3), and the power factor (pf):

[

P = √3 \cdot V \cdot I \cdot pf

]

Rearranging this formula to solve for current gives:

[

I = \frac{P}{√3 \cdot V \cdot pf}

]

Here, the power (P) is 186.84 kW (or 186,840 W), and the power factor is 0.75. To find the current, we also need the line voltage (V) of the generator. However, since this is a multiple-choice question, we can deduce the current assuming typical voltages used in three-phase systems, often around 400V.

Inserting our values into the rearranged equation, we can take the most common scenarios of line voltage to try and achieve the answers provided. When we include a typical line voltage of