A three-phase induction motor is rated at 5 hp, 1760 rpm, with a line-to-line voltage of 220 V r

step 1 In this problem, p out is equal to 5 -hp which is equal to 5 multiplication 746 which is equal t

A three-phase induction motor is rated at 5 hp, 1760 rpm,...

A three-phase induction motor is rated at $5 \mathrm{hp}, 1760 \mathrm{rpm},$ with a line-to-line voltage of $220 \mathrm{V} \mathrm{rms}$. The motor has a power factor of 80 percent lagging and an efficiency of 75 percent under full-load conditions. Find the electrical input power absorbed by the motor under full-load conditions. Also. find the rms line current.

Key Concepts

Three-Phase Power Calculation

In three-phase electrical systems, the total real power delivered to a load is calculated using the formula P = ?3 × V_line × I_line × power factor. This relationship, which incorporates the line-to-line voltage and the appropriate phase current, is essential when analyzing balanced loads such as induction motors.

Motor Efficiency

Motor efficiency is the ratio of the output mechanical power to the electrical input power, typically expressed as a percentage. It indicates how effectively the motor converts electrical energy into mechanical work and is used to determine the actual electrical power consumption from a given mechanical power rating.

Power-to-Horsepower Conversion

Horsepower is a unit used to express the mechanical power output of motors. In many calculations, it is necessary to convert horsepower to watts (with 1 horsepower approximately equal to 746 watts) to maintain consistency in units when using SI units for power calculations.

Power Factor

The power factor is the ratio of the real power that performs useful work to the apparent power that flows in the circuit. A lagging power factor, common in inductive loads such as motors, indicates that the current is out of phase with the voltage, which affects the overall current consumption and efficiency of the power system.

RMS (Root Mean Square) Values

RMS values represent the effective magnitude of alternating current or voltage, equivalent to a direct current value that would deliver the same power. They are used in AC power calculations to ensure accurate determination of power and current, especially in the context of three-phase systems where both the line-to-line voltage and phase currents are given as RMS values.

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