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The first number indicates the size of the wires, in this case #10 AWG (American Wire Gauge). The last number refers to the quantity of conductors, excluding the ground wire, if any. 10-2 wire would have two conductors, typically a black used for the hot, and a white used for the neutral. If the label says "10-2 with ground" then the cable would also contain a bare or green insulated ground wire. 10-3 wire contains all the above plus one more wire, typically red, used for an additional hot.

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Q: What the difference between 10-2 wire and 10-3?
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