The mechanism of the heat produced in a conductor when an electric current flows through it, can be explained on the basis of
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Free electron theory:

In metals, most atoms have loosely bound electrons in their outermost orbits, known as free electrons since they have a real nice tendency to detach from their parent atom and move freely. The charge flow occurs due to the movement of electrons. In the presence of an external electric field, all the free electrons would flow in a direction opposite to the field thus constituting a current.

As the electrons move through the metal conductor, some collide with atoms and other electrons or impurities. These collisions cause resistance and generate heat in the conductor.

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