Question

An ac motor with impedance ZL=(5.6+2.20)Ω is supplied by an RMS value of 220−V,60−Hz source. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the capacitor required to be connected in parallel with the motor so that the power factor is corrected to unity. The required value of the capacitor is μF.

Answer 1

To correct the power factor to unity for an AC motor, calculate the reactive power based on the motor's inductive reactance and supply voltage, determine the necessary capacitive reactance, and use it to find the required capacitance value in microfarads.

Step-by-step explanation:

To determine the capacitor required to be connected in parallel with the motor so that the power factor is corrected to unity, we first need to calculate the reactive power (Q) of the inductive load. The motor's impedance is given as ZL = (5.6 + j2.20)Ω. The inductive reactance (XL) part of ZL is 2.20Ω, and we can calculate Q using the formula Q = VRMS2 / XL, where VRMS is the RMS voltage of the supply which is 220V.

After calculating Q, we can find the capacitive reactance (XC) needed to cancel out this reactive power, using XC = -VRMS2 / Q. Then we use the formula XC = 1 / (2πfC) to find the capacitance (C), where f is the frequency (60 Hz) of the AC supply.

Finally, we rearrange the formula to solve for C: C = 1 / (2πfXC), and convert the capacitance into microfarads (µF).