An induction motor has 40kVA input power, a power factor of 82 percent, and an efficiency of 92 percent. What is the horsepower?

To determine the horsepower of the induction motor, it is essential to first convert the motor's input power from kVA to kilowatts (kW), since horsepower is a measure of power, and we can relate it directly to kW.

Given the input power of 40 kVA along with a power factor of 82%, we convert the apparent power (kVA) to real power (kW) using the formula:

Real Power (kW) = Apparent Power (kVA) × Power Factor

So, we calculate:

Real Power (kW) = 40 kVA × 0.82 = 32.8 kW

Next, we need to account for the efficiency of the motor to find the output power. The efficiency tells us what portion of the input power is converted to useful output power. With an efficiency of 92%, the output power (kW) can be calculated using the formula:

Output Power (kW) = Input Power (kW) × Efficiency

Now, we first convert the input power from kVA to kW (already calculated above) and apply efficiency:

Output Power (kW) = 32.8 kW × 0.92 = 30