HYPOTTHETICAL question. If I hade a motor that hade 50% power factor and the amps draw was 3 amps @ 120 v and watts were 185 would the voltage drop on the wire be the same as a motor with about 100% power factor that pulled 3 amps and 350 watts ?
Good question. I do not have an exact answer for you. I will venture a guess and say that the voltage drop will be less on the lower power factor circuit. This is because the voltage and current are not in phase.
If you measure the voltage across the section of wire with the 3 A of current flow in it, then the drop along that wire is the same independent of the load power factor.
However, if you define voltage drop as the change in voltage at the load point from no load to loaded, then when the load is not unity power factor you need to do a vector calculation to determine voltage drop.
For small voltage drops it does not make much difference.