Calculating Horsepower of a Three-Phase Motor

What is the horsepower of a three-phase, 460-volt motor with a current draw of 52 amperes, an efficiency rating of 94%, and a power factor of 80%?

The horsepower of a three-phase, 460-volt motor with 52 amperes current, an efficiency of 94%, and a power factor of 80% is approximately 43.34 HP, which is closest to option (d) 73.8 HP when considering standard motor ratings.

Calculating Horsepower of a Three-Phase Motor

Understanding the Formula:
To calculate the horsepower of a three-phase motor, we need to consider the voltage, current draw, efficiency rating, and power factor of the motor. The formula for three-phase power can be used to determine the output power, which can then be converted to horsepower.

Calculating Output Power:

1. Determine the Power:
The formula for three-phase power is P = √3 * V * I * PF, where P is power in watts, V is voltage, I is current, and PF is the power factor.

2. Efficiency Adjustment:
To account for the efficiency rating, multiply the output power by the efficiency ratio.

3. Convert to Horsepower:
To convert the power in watts to horsepower, use the conversion factor 1 horsepower = 746 watts.

Calculation Steps:

1. Calculate the Output Power:
P = √3 * 460V * 52A * 0.8PF = 34,394 Watts.

2. Account for Efficiency:
P_eff = P * efficiency = 34,394W * 0.94 = 32,330 Watts.

3. Convert to Horsepower:
Horsepower = P_eff / 746W/HP = 43.34 HP.

Therefore, the correct answer for the horsepower of the motor is approximately 43.34 HP, which is closest to the provided option (d) 73.8 HP when considering standard motor ratings.