Approximately how many kilowatts does a three-phase, 480-volt AC motor that draws a current of 52 amperes and has a power factor of 88% use?

Approximately how many kilowatts does a three-phase, 480-volt AC motor that draws a current of 52 amperes and has a power factor of 88% use?

• A. 25 kW
• B. 30 kW
• C. 38 kW
• D. 45 kW

Answer: (C)

To determine the kilowatts used by a three-phase, 480-volt AC motor with a current of 52 amperes and a power factor of 88%, we can utilize the formula for calculating power in a three-phase system: \[ P = \sqrt{3} \times V \times I \times PF \] Where: - \( P \) is the power in watts, - \( V \) is the voltage, - \( I \) is the current in amperes, - \( PF \) is the power factor (expressed as a decimal). First, we need to convert the power factor from a percentage to a decimal. An 88% power factor translates to 0.88. Now we can substitute the known values into the formula: \[ P = \sqrt{3} \times 480 \, \text{V} \times 52 \, \text{A} \times 0.88 \] Calculating step by step: 1. Calculate \( \sqrt{3} \), which is approximately 1.732. 2. Multiply \( 1.732 \) by \( 480 \) (the voltage): \[ 1

To determine the kilowatts used by a three-phase, 480-volt AC motor with a current of 52 amperes and a power factor of 88%, we can utilize the formula for calculating power in a three-phase system:

[

P = \sqrt{3} \times V \times I \times PF

]

Where:

• ( P ) is the power in watts,

• ( V ) is the voltage,

• ( I ) is the current in amperes,

• ( PF ) is the power factor (expressed as a decimal).

First, we need to convert the power factor from a percentage to a decimal. An 88% power factor translates to 0.88. Now we can substitute the known values into the formula:

[

P = \sqrt{3} \times 480 , \text{V} \times 52 , \text{A} \times 0.88

]

Calculating step by step:

1. Calculate ( \sqrt{3} ), which is approximately 1.732.

2. Multiply ( 1.732 ) by ( 480 ) (the voltage):

[

1