Question

Does a conductor become charged when a current is passed through it?

Answer 1

No, a conductor does not become charged when a current is passed through it. The free electrons present in the valence shell in a circuit drift  from a lower potential to a higher potential and, thus, current is produced. A battery does not provide any extra electrons or charge to the circuit. It just provides a potential difference across two points, which helps in creating an electric field. This further helps in moving the electrons along the conductor.