The voltage drop in a cable is the current multiplied by the resistance. For a twin-wire cable the resistances of the two wires are added. Cable resistance for different sizes of cables can be looked up in wire tables.
More detailed answer for USA, Canada and countries running a 60 Hz supply service.
Voltage drop and cable size can be calculated by looking at tables that are available in the National Electrical Code. Some of these tables are difficult to understand and will require you to seek assistance. You can also determine the amount of voltage drop over a distance by finding the resistance of the cable for a specific temperature(given in ohms/1000ft)from the cable manufacturer or electrical wholesaler. If you know the largest amount of current that will flow in the cable, then use the formula:
Vdrop = Current X Distance(Ft) X 2 X Ohms per 1000Ft x 0.001
[Note: the 0.001 fixes an earlier error in the formula where the contributor didn't divide out 1000 ft by using R/1000ft!]
Voltage drop is a complicated calculation done by electricians. I don't know what you're trying to run but let me just give you the rule of thumb. If you run out over 200 feet of wire for the job in hand, you should jump up a wire size in order to have sufficient voltage at the other end. For example. Let's say you are going to wire and out building for your workshop and you need only 120 volt receptacles at the shop end to run your power tools. Power tools run at the nominal voltage of 120 volts, but they operate within a range, say 108 to 128. This allows for how close your are to your distribution companies source. I don't know what your starting voltage is so that's why the rule of thumb. To your outbuilding you only need #12 to carry 20 amps for your tools and lights etc. If you have to exceed that distance, then you would jump up to #10 in order to have sufficient voltage at the other end. If you are starting at 115 volts at your house, and are running 100 feet, I would still up the wire size. You can't go wrong by going one size bigger on your wire. When in doubt, always consult a qualified electrician.
Many electricians wire for no more than 5% voltage drop. This is usually fine since appliances and power tools are made to operate over a range of voltages. For a more expensive way to wire a house, you can try wiring for no more than 2% voltage drop. In this case, if you are running 20 amps, you need to up the wire size to #10 if you go more than 35 feet. In general, the percentage voltage drop decreases with a higher starting voltage. To see this, play around with the formula for voltage drop given in terms of resistance. The resistance of various sizes of wires can be found in the CRC handbook. Practically, this means you lose less power to voltage drop if you choose a 240 volt appliance instead of a 120 volt one. And you lose a lot with low voltage lighting running on 10 or 12 volts.
The formula for voltage drop is Vd=KIL/CSA where Vd stands for voltage drop, K stands for the resistivity factor of the material [I think copper is around 7 and aluminum 11], I is the current in Amperes, L is the round trip length of conductor, CSA is cross-sectional area of the conductor in circular mils
You can get the CSA values from chapter 9 table 8 of the NEC
CSA for 14 is 4,110; 10 is 10,380; 8 is 16,510; 6 is 26,240
As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.
Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized.
IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.
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