A 1-hp 120-V-rms 1740-rpm 60-Hz capacitor-start induction-run motor draws a current of 10.2 A rm

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A 1-hp 120-V-rms 1740-rpm 60-Hz capacitor-start...

A $1-\mathrm{hp}$ $120-\mathrm{V}-\mathrm{rms}$ $1740-\mathrm{rpm}$ $60-\mathrm{Hz}$ capacitor-start induction-run motor draws a current of $10.2 \mathrm{A}$ rms at full load and has an efficiency of 80 percent. Find the values of a. the power factor and b. the impedance of the motor at full load. c. Determine the number of poles that the motor has.

Key Concepts

Power Factor

Power factor is the ratio of the real (active) power that is used to do useful work to the apparent power flowing in an AC circuit. It indicates how efficiently the current is being converted into useful work output and is defined as the cosine of the phase angle between the voltage and current waveforms.

Efficiency

Efficiency is the measure of how well an electrical machine converts input electrical energy into output mechanical energy. It is expressed as a percentage, calculated by dividing the useful output power by the input power, and plays a key role in determining the actual power consumed by the device.

Real and Apparent Power

Real power, measured in watts (W), is the power that performs actual work in a circuit, while apparent power, measured in volt-amperes (VA), is the product of the RMS voltage and current irrespective of phase angle. Understanding the relationship between these two concepts is essential, as the ratio of real power to apparent power directly gives the power factor.

AC Circuit Impedance

Impedance in AC circuits is the total opposition that a circuit presents to the flow of alternating current, and it is expressed in ohms. It is a combination of resistance and reactance (which includes both capacitive and inductive effects) and can be calculated as the ratio of the RMS voltage to the RMS current in the circuit.

Synchronous Speed and Motor Poles

Synchronous speed is the speed at which the magnetic field rotates in an AC motor, and it is defined by the supply frequency and the number of poles in the motor using the formula: synchronous speed (in rpm) = (120 × frequency) / (number of poles). This concept helps in determining the motor's construction, since the actual rotor speed is slightly lower due to slip.

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