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The American Wire Gauge code table shows 8 gauge safe for 24 Amps, 10 Gauge for 15 Amps. If the circuit is going to be used at capacity (2400 Watts in this case), 8 or 10 gauge is the minimum, if load is constant, use 8 gauge.

Voltage ability of the wire is dependent on the insulation thickness and material. So 20 amps at 120 Volts is 2400 watts of power, and 20 amps at 12 volts is 48 watts of power. Both would require the same gauge of wire, but the higher voltage would need better insulation.

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This is a voltage drop question.

A #1 copper conductor will limit the voltage drop to 3% or less when supplying 20 amps for 500 feet on a 120 volt system.

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