Question

Required informotion An ac motor with impedance Z L={3.2+μ1.60}Ω is supplied by an RMS value of 220−V,60+Hz source. NOTE. This is a multi-part question. Once an answer is subinitted, vou will be unable to return to this part.

Find the power factor, the average power, and the reactive power.
The power factor of the given ac motor is _____
The average power of the given ac motor is ____ kW.
The reactive power of the given ac motor is ____ kVAR.

Answer 1

The power factor, average power, and reactive power of an AC motor with given impedance and RMS voltage can be calculated using the formulas for power factor (PF = R / |Z|), average power (Pave = Vrms^2 * PF / R), and reactive power (Q = Vrms * Irms * sin(φ)), respectively.

Step-by-step explanation:

The power factor, the average power, and the reactive power of an AC motor with impedance ZL = {3.2 + j1.60} Ω supplied by a 220 V RMS, 60 Hz source can all be determined from the given impedance and voltage.

Power Factor Calculation:

The power factor (PF) is the ratio of the resistance (R) to the magnitude of the impedance (|Z|). The magnitude of Z is √(R^2 + (XL - XC)^2). Since the motor doesn't seem to have capacitive reactance (XC), the power factor formula simplifies to:

PF = R / |Z| = 3.2 Ω / √(3.2^2 + 1.6^2) Ω

Average Power Calculation:

The average power (Pave) is given by Pave = Vrms^2 * PF / R. Upon solving this with the given voltage and calculated PF, we find the average power in kilowatts.

Reactive Power Calculation:

The reactive power (Q) is the product of the RMS voltage, the RMS current, and the sine of the phase angle, which corresponds to Q = Vrms * Irms * sin(φ). Since sin(φ) in this case is equivalent to the imaginary part of the impedance over the magnitude of the impedance, we can calculate the reactive power in kilovolt-amperes reactive (kVAR).