What is the power factor on a 480-volt, 60-horsepower, 3-phase motor with an efficiency of 85% when the full load current is 70 amperes?
The Correct answer and Explanation is:
To calculate the power factor of a 480-volt, 60-horsepower (HP), 3-phase motor with an efficiency of 85% and a full load current of 70 amperes, we need to break down the problem into steps. The power factor (PF) is the ratio of real power (P) to apparent power (S), expressed as:
[ \text{Power Factor} (PF) = \frac{\text{Real Power} (P)}{\text{Apparent Power} (S)} ]
Step 1: Convert Horsepower to Watts
First, convert the motor’s power rating from horsepower to watts. The formula to convert HP to watts is:
[ \text{Power (Watts)} = \text{Horsepower} \times 746 ]
For a 60 HP motor:
[ \text{Power (Watts)} = 60 \times 746 = 44,760 \, \text{Watts} ]
Step 2: Account for Efficiency
Efficiency represents how much of the input power is converted into useful output power. The motor’s efficiency is 85%, so the input power can be calculated as:
[ \text{Input Power} = \frac{\text{Output Power}}{\text{Efficiency}} ]
For this motor:
[ \text{Input Power} = \frac{44,760 \, \text{Watts}}{0.85} = 52,659 \, \text{Watts} ]
Step 3: Calculate Apparent Power (S)
The apparent power is calculated using the formula for 3-phase systems:
[ S = \sqrt{3} \times V \times I ]
Where:
- ( V ) is the line voltage (480 volts),
- ( I ) is the full load current (70 amperes),
- ( \sqrt{3} \approx 1.732 ).
Thus:
[ S = 1.732 \times 480 \times 70 = 58,185 \, \text{Volt-Amperes (VA)} ]
Step 4: Calculate the Power Factor (PF)
Now, we calculate the power factor by dividing the real power (input power) by the apparent power:
[ PF = \frac{52,659}{58,185} \approx 0.905 ]
Conclusion
The power factor of this motor is approximately 0.905. This means that about 90.5% of the apparent power is being effectively used for productive work, while the rest is reactive power. A power factor close to 1 is ideal for efficient electrical systems, and this motor has a relatively good power factor.