To calculate voltage drop in a copper wire, use the following formula:
Volts= Length x Current x 0.017
Volts= Voltage drop.
Length= Total Length of wire in metres (including any earth return wire).
Current= Current (amps) through wire.
Area= Cross sectional area of copper in square millimetres.
• This formula only applies to copper at 25°C, voltage drop increases with wire temperature, at approx 0.4% per °C.
• 0.017- This figure only applies to copper.
• Area is in square millimetres of copper, there can be confusion on how cable size is rated, with some manufacturers stating wire diameter rather than area, some even including the insulation. An explanation of this can be seen at here.
A trailer has 50M of 4 square mm wire so, how much voltage drop at 20A?
50 x 20 x 0.017= 17. Divide this by 4 (cross section area of wire): 17/4= 4.25V.
In this example, the drop is 4.25V. This would mean that if there was 12V at the front of the trailer, there would only be 7.75V at the back - the lights would be very dim.
This is when the wire temp is 25ºC, if the wire temp was 35ºC there would be a 4.42V drop, meaning only 7.37V at the back of the trailer.
Don't forget that the current through the wire will heat it up,so even if it is only a 25ºC day, the wire will be hotter, which will increase the voltage drop.
This will keep increasing until the cooling effect of the surrounding air on the wire balances the heating effect of the current.
This demonstrates why it is important not to skimp on wire size when wiring a trailer.