Final answer:
The power factor of a 100-hp electric motor is calculated using real power output derived from the motor's horsepower and efficiency, and apparent power calculated from voltage, current, and the fact it's a three-phase motor. The calculation leads to a power factor of approximately 0.774. High-performance motors with high power factors are important for energy efficiency and reducing operational costs.
Step-by-step explanation:
The student asked for the calculation of the power factor of a 100-hp electric motor with specified parameters. The power consumed by an electric motor is given by the formula P = IVcosφ where P is the power, I is the current, V is the voltage, and cosφ is the power factor. Given the motor's efficiency, we can find the actual power output and then use the current and voltage to calculate the power factor.
To calculate the real power output (Poutput) of the motor, we use the motor's horsepower and the efficiency: Poutput = horsepower × 746 W/hp × efficiency. With the motor rated at 100 hp and 95% efficiency, Poutput = 100 hp × 746 W/hp × 0.95 = 70,870 W.
The apparent power (S) consumed by the motor is the product of the RMS voltage (V), the RMS current (I), and √3 (since it's a three-phase motor): S = V × I × √3 = 460 V × 114 A × √3 ≈ 91,514 VA.
Finally, the power factor (cosφ) is the ratio of the real power output to the apparent power: cosφ = Poutput / S = 70,870 W / 91,514 VA ≈ 0.774.
It is important to use high-performance motors because they are more efficient in converting electrical energy into mechanical energy, thus saving energy and reducing operational costs over time. A motor with a power factor significantly less than 1 would draw more current to do the same work, leading to higher energy consumption. Improving the power factor is a more efficient way to enhance motor output rather than increasing the voltage input, as it reduces the energy losses in power transmission and distribution systems.