What is the relationship between mechanical and electrical power?

What is the relationship between mechanical and electrical power?

• A. 1 horsepower equals 1000 watts
• B. 1 horsepower equals 746 kilowatts
• C. 1 horsepower equals 746 watts
• D. 1 horsepower equals 0.746 watts

Answer: (C)

Power is the rate at which work is done, and the watt is the standard SI unit for that rate. A horsepower is defined as 550 foot-pounds of mechanical work per second. Converting to SI: 1 ft-lb is about 1.3558 joules, so 550 ft-lb per second is about 745.7 joules per second, i.e., 745.7 watts. That’s why we say 1 horsepower is about 746 watts. In electrical terms, the input power is P = V × I (for DC) or P = VI cosφ (for AC), and the mechanical power a motor delivers is P_mech = η × P_in, where η is efficiency. So 1 hp corresponds to roughly 746 W of mechanical power when everything is efficient. The other options mix up magnitudes or units, so they don’t match the standard conversion.

Power is the rate at which work is done, and the watt is the standard SI unit for that rate. A horsepower is defined as 550 foot-pounds of mechanical work per second. Converting to SI: 1 ft-lb is about 1.3558 joules, so 550 ft-lb per second is about 745.7 joules per second, i.e., 745.7 watts. That’s why we say 1 horsepower is about 746 watts. In electrical terms, the input power is P = V × I (for DC) or P = VI cosφ (for AC), and the mechanical power a motor delivers is P_mech = η × P_in, where η is efficiency. So 1 hp corresponds to roughly 746 W of mechanical power when everything is efficient. The other options mix up magnitudes or units, so they don’t match the standard conversion.