Final answer:
To find the power factor of a 480-volt, 60-horsepower, 3-phase motor with an efficiency of 85% and full load current of 70 amperes, use the power formula P = √3 × V × I × PF × Efficiency. Convert horsepower to watts, then calculate the power factor by rearranging the formula to solve for PF.
Step-by-step explanation:
To calculate the power factor of a 480-volt, 60-horsepower, 3-phase motor, we must first understand the relationship between horsepower, efficiency, and power factor in electrical motors. The power factor (PF) is the ratio of real power used to do work (in watts) and the apparent power (in volt-amperes) flowing through the circuit.
In a 3-phase system, the formula to calculate the real power (P) in watts (W) is:
P = √3 × V × I × PF × Efficiency
Where V is the voltage in volts (V), I is the current in amperes (A), and Efficiency is the motor's efficiency as a decimal.
To find the power factor, we rearrange the formula:
PF = P / (√3 × V × I × Efficiency)
We know the horsepower (HP) of the motor is 60, the full-load current (I) is 70 amperes, and the efficiency is 85% or 0.85 in decimal form. First, we convert horsepower to watts because the standard conversion is 1 HP = 746 W.
P = 60 HP × 746 W/HP = 44760 W
Now we can plug in the numbers to the power factor formula:
PF = 44760 W / (√3 × 480 V × 70 A × 0.85)
After calculations, you will get the power factor that the motor operates at with the given parameters.