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The wire to use would be one that can handle the 3 amp capacity of the load. If the load is a long ways away increase the wire size. A #14 wire has the capacity to handle 15 amps.

Depends on how far you're running it and what voltage drop you can tolerate.

I would use 14 gauge, minimum. That will give less than 10% voltage drop on a copper pair running 50 feet.

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