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The amount of heat produced in a wire depends on the resistance of the wire and the amount of current through it. As long as the current is less than the capacity of the wire, the heat will be small enough that it can dissipate into the surroundings at the same rate that it is produced, so the temperature of the wire will not rise more than a few degrees. If the current exceeds the capacity of the wire, the heat produced cannot be carried away quickly enough and the temperature of the wire will rise rapidly.

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