A three-phase, 460-volt motor draws a current of 52 amperes. What is the horsepower if it has an efficiency rating of 94% and a power factor of 80%?

To determine the horsepower output of a three-phase motor, we first need to calculate the input power in watts using the formula for three-phase systems:

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

Where:

• ( V ) is the line voltage (460 volts)

• ( I ) is the current (52 amperes)

• Power Factor is 0.80

Calculating the input power:

1. Find the apparent power in watts:

[ P = \sqrt{3} \times 460, \text{V} \times 52, \text{A} \times 0.80 ]

[ P = 1.732 \times 460 \times 52 \times 0.80 ]

[ P \approx 1.732 \times 460 \times 52 \times 0.80 \approx 61,317.7, \text{W} ]

2. Next, since the motor has an efficiency rating of 94%, we can find the actual useful power output (useful power output is the input power multiplied by efficiency):

[ \text{Output Power} = P \times \