A 1-horsepower, 24-volt DC motor that is 80 percent efficient requires 932.5 watts. How much power will a 1-horsepower, 12-volt DC motor that is 75 percent efficient require?

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Multiple Choice

A 1-horsepower, 24-volt DC motor that is 80 percent efficient requires 932.5 watts. How much power will a 1-horsepower, 12-volt DC motor that is 75 percent efficient require?

Explanation:
The key idea is the relation between input power, output power, and efficiency: η = P_out / P_in, so P_in = P_out / η. A mechanical output of 1 horsepower equals 746 watts. If the motor is 75% efficient, it needs P_in = 746 / 0.75 ≈ 994.7 watts of electrical power to deliver that 1 HP. The voltage doesn’t change the required input power for the same mechanical output; it would only affect current drawn (I = P_in / V). So the correct amount of power required is about 994.6 watts.

The key idea is the relation between input power, output power, and efficiency: η = P_out / P_in, so P_in = P_out / η. A mechanical output of 1 horsepower equals 746 watts. If the motor is 75% efficient, it needs P_in = 746 / 0.75 ≈ 994.7 watts of electrical power to deliver that 1 HP. The voltage doesn’t change the required input power for the same mechanical output; it would only affect current drawn (I = P_in / V). So the correct amount of power required is about 994.6 watts.

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