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Copper conducts electricity by "musical electrons" like other conductors do. Let's look at copper and see what's up. Copper atoms in a copper wire all form some kind of metallic crystal structure. Not all the electrons in the valence shells of the copper atoms are "locked in place" in this structure. They are free to move around, and are said to be "free electrons" in this application. As they are not "bound" in the structure, the electrons can be made to move fairly easily. They can contribute to current flow. If we apply a voltage across the wire from end to end, electrons will enter one end of the wire and electrons will emerge from the other. Not the same electrons, mind you. Put some in one end, some come out the other. It could also be said that some of the electrons of the copper are at Fermi energy levels that are in what is said to be the "conduction band" for copper. The conduction band is the minimum energy level necessary for electrons of a given material to be in to support conduction in that material. If the Fermi energy levels of the valence band electrons is up in the conduction band, then that material is a conductor. Copper is this way.

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Q: How does copper conduct electricity?
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