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running electric 740 ft how many amps can I run that far? Answered

I want to run electric back to a cabin in the woods its about 740 ft from power source.  What cable do I use and do I need a step up transformer to get more amps back to cabin? What size wire for at least 20 amps +  to reach cabin? Power source is 30 amp

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I would go up one size just for kink heat and strength so instead of #7 I would use #6.

If you run it on top of the ground, the cable can be damaged from being run over or rodents chewing on the wire.

Run it under the ground in a conduit, or in the air with a support cable.

https://en.wikipedia.org/wiki/American_wire_gauge#...

For long wires, the main problem is voltage drop. How much drop is too much?

Well, just to get you started, suppose the voltage at the source is 120 Vrms, and the maximum drop you will allow is 12 Vrms, which is 6 volts per wire, in each direction. (Note this corresponds to a 10% loss of voltage, and power; 10 percent of your total power bill is going to heating copper wire.)

The long wire is essentially a resistor, and can be modeled by Ohm's law. The voltage drop across the long wire is proportional to the current running through it.

V = I*R,

and R= V/I, so the maximum allowable resistance per wire, in each direction, is

R= (6V)/( 30 A) = 0.20 ohm

Next divide this number by 740 feet, to get

(R/L) = (0.20 ohm)/(740 feet) = 0.00027 ohm/foot = 0.27 mohm/foot

Next, look in the table for the wire size with (R/L) a little less than that, which looks like 4 AWG, at 0.2485 mohm per foot.

This is kind of a dissapointing result, since 4 AWG is some rather thick wire, and expensive too, compared to smaller gauges.

Maybe if you relax your criteria for voltage drop, allowing 24 Vrms, and only use half as much current, 15A instead of 30, then you could increase (R/L) by a factor of 4, to get 1.08 mohm/foot, which would be satisfied with 10 AWG wire.