At what voltage does a three-phase generator operate if it delivers 220 A with a power factor of 0.8 and the real power output is calculated to be 166.08 kW?

At what voltage does a three-phase generator operate if it delivers 220 A with a power factor of 0.8 and the real power output is calculated to be 166.08 kW?

• A. 600 V
• B. 480 V
• C. 240 V
• D. 120 V

Answer: (A)

To determine the operating voltage of the three-phase generator, we can utilize the formula for real power in a three-phase system: \[ P = \sqrt{3} \times V \times I \times \text{PF} \] Where: - \( P \) is the real power in watts (W), - \( V \) is the line-to-line voltage in volts (V), - \( I \) is the current in amperes (A), - \( \text{PF} \) is the power factor (a unitless number between 0 and 1). Given that the real power output \( P \) is 166.08 kW, we first convert that to watts: \[ 166.08 \, \text{kW} = 166080 \, \text{W} \] The current \( I \) is given as 220 A, and the power factor \( \text{PF} \) is 0.8. We need to solve for \( V \): 1. Rearranging the formula to solve for \( V \): \[ V = \frac{P}{\sqrt{3} \times I \times \text{PF}} \] 2

To determine the operating voltage of the three-phase generator, we can utilize the formula for real power in a three-phase system:

[ P = \sqrt{3} \times V \times I \times \text{PF} ]

Where:

• ( P ) is the real power in watts (W),

• ( V ) is the line-to-line voltage in volts (V),

• ( I ) is the current in amperes (A),

• ( \text{PF} ) is the power factor (a unitless number between 0 and 1).

Given that the real power output ( P ) is 166.08 kW, we first convert that to watts:

[ 166.08 , \text{kW} = 166080 , \text{W} ]

The current ( I ) is given as 220 A, and the power factor ( \text{PF} ) is 0.8. We need to solve for ( V ):

1. Rearranging the formula to solve for ( V ):

[ V = \frac{P}{\sqrt{3} \times I \times \text{PF}} ]

2