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Because the wire has resistance.

The power (number of watts) dissipated by any resistance when current passes through it is

(the number of amperes of current)2 multiplied by (the number of ohms of resistance).

To reduce the power lost from the wire, the choices are:

-- reduce the current passing through the wire

-- use thicker wire

-- keep the wire as cold as possible.

(If the wire is made of the right material, and you make it cold enough,

then all of its resistance disappears, and it's called a "superconductor".)

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Q: Why does a wire get hot when an electric current passes through it?
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