An AC motor with 3 hp output power 230 V angle 0 degree inpu

An AC motor with 3 hp output power, 230 V angle 0 degree input voltage, 1450 r/min speed, 60 Hz frequency has the following information: full-load current: 10 A, efficiency: 85 %, power factor: 86%, weight: 80 lb Calculate the active, reactive, and apparent power absorbed by this machine when it operates at full load. (P=2632 W, Q=1562VAr, S=3061VA) If a 30 mu Farad capacitor is connected across the motor terminals, calculate the new power factor (93%) Calculate the line current that motor draws after the capacitor connection. (12.19A) Calculate the amount of current change in percentage after the capacitor connection (21%)

Solution

Efficiency =0.85 so

Motor input power (active power)=output/efficiency=(3*745.6/0.85)=2632watts.

Given power factor=0.86 so appreant power =(2632/0.86)=3061VA

Reactive power=(appreant power)^2--(active power)^2 =1562VAR

B) capacitive reactive power = V^2/Xc=598.2VAR

So net reactive power=1562-598.3=962.7 VAR

New apparent power=2802VA

New power factor=cos(arcsin(reactive power/apparent power)=0.932

C)line current=[2632/(3*230*0.93)]=12.19A

D) change in current=(12.19-10)/10=21%