Calculate the power factor of 3 motors connected in parallel?
Three motors run in parallel from an a.c. supply. One motor takes 12A at a power factor of 0.4, and another takes 16A at a power factor of 0.8. If the total current is 40A at a power factor of 0.6, determine the current and power factor of the third motor?
There might be a short way of doing this, but all I can think of right now is to solve it as a plain old AC steady-state problem. Draw the three motors in parallel, assume a voltage of, oh, 100 volts AC, and write in the currents. You know the phases of the currents because you know the power factor of each motor, and you know the total current through the voltage source, and you know its phase. Put all the currents into rectangular form and do the appropriate arithmetic to find the phase angle of the third motor’s current and thus its power factor.
