What is the line current of a 7 horsepower motor operating on 120 volts at full load, with a power factor of 0.8, and 95% efficiency?

To determine the line current for a 7 horsepower motor operating at 120 volts with the specified power factor and efficiency, we can use the following steps.

First, convert horsepower to watts. Since 1 horsepower is equal to 746 watts, a 7 horsepower motor operates at:

[

\text{Power (P)} = 7 , \text{hp} \times 746 , \text{watts/hp} = 5222 , \text{watts}

]

Next, because the motor is not 100% efficient, we need to account for its efficiency. The actual input power required by the motor at full load can be calculated by dividing the output power by the efficiency:

[

\text{Input Power} = \frac{5222 , \text{watts}}{0.95} \approx 5507.37 , \text{watts}

]

After calculating the input power, we can determine power in terms of apparent power (in volt-amperes) considering the power factor (pf) of 0.8:

[

\text{Apparent Power (S)} = \frac{\text{Input Power}}{\