A three-phase, 460-volt motor draws a current of 52 amperes with an efficiency of 94% and a power factor of 80%. What is the horsepower?

A three-phase, 460-volt motor draws a current of 52 amperes with an efficiency of 94% and a power factor of 80%. What is the horsepower?

• A. 24.1 hp
• B. 41.7 hp
• C. 50.0 hp
• D. 73.8 hp

Answer: (B)

In a three-phase system, the real power drawn by the motor is P_in = √3 × V × I × pf. The motor’s useful mechanical power output is P_out = P_in × efficiency. To get horsepower, convert watts to hp using 1 hp ≈ 746 W. Plugging in the values: √3 ≈ 1.732, V = 460 V, I = 52 A, pf = 0.80, efficiency = 0.94. P_in = 1.732 × 460 × 52 × 0.80 ≈ 33,144 W P_out = 33,144 × 0.94 ≈ 31,155 W HP = 31,155 / 746 ≈ 41.7 hp So the motor delivers about 41.7 horsepower. The pf and efficiency are essential: pf gives the real power used by the motor, and efficiency converts that electrical power into usable mechanical power; ignoring either would misestimate the horsepower.

In a three-phase system, the real power drawn by the motor is P_in = √3 × V × I × pf. The motor’s useful mechanical power output is P_out = P_in × efficiency. To get horsepower, convert watts to hp using 1 hp ≈ 746 W.

Plugging in the values: √3 ≈ 1.732, V = 460 V, I = 52 A, pf = 0.80, efficiency = 0.94.

P_in = 1.732 × 460 × 52 × 0.80 ≈ 33,144 W

P_out = 33,144 × 0.94 ≈ 31,155 W

HP = 31,155 / 746 ≈ 41.7 hp

So the motor delivers about 41.7 horsepower. The pf and efficiency are essential: pf gives the real power used by the motor, and efficiency converts that electrical power into usable mechanical power; ignoring either would misestimate the horsepower.