If we had a 1/2 horsepower motor designed to run on 120 volts, nominal, with a F.L.C. of 9.8 amp as per NEC Table 430-148 , and we lost the 3.6 volts due to a long distance run causing the above calculated voltage drop this motor would now be pulling at the full load amps as follows;
Special Notes: You must change the Amps into Volt-Amps, in order to accomplish the conversion, in the change of voltage, due to the voltage drop calculated above.
9.8 AMPS x 120 VOLTS = 1,176 VOLT AMPS
1,176 VA DIVIDED BY 116.4 VOLTS AT END OF LINE = 10.103 AMPS
Formula to change amps into approximate volt - amps = amps x volts = volt amps
Example of Voltage Drop, Approximate "K" And Exact "K"
Calculating the Resistance of a Conductor = (K) (Approximate K & Exact K)
Approximate K = 12.9 for copper.
Approximate K = 21.2 for aluminum
VD=2xKxDxI/Cm
I= Current
2= round trip loss (you'd use 1x if it was a balanced wye circuit)
KxD/Cm represents the resistance of this wire.
Voltage Drop = 2x Current x Resistance
D=length of wire
K/Cm=resistance per unit length.
K is the unit resistance of copper per circular mil
Cm is circular mills of the conductor. (roughly 2.8 Ohms/kcmil/100 feet DC) This equation is only accurate for DC. You can approximate AC (K is roughly 1.3 for AC), but it varies by cable size due to skin resistance and isn't terribly accurate.
Really, you should also be adjusting it forpower factor and the type of conduit it's in and wire temperature, too, but usually if you have to go into that much detail, you should be upsizing anyhow.
http://www.paigeelectric.com/tools/metric_awg_conversion.aspx