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Consider a simple DC circuit composed of a battery (say 2V), conducting wires and a single resistor R=2 Ohm

The potential difference across the resistor will be exactly 2V only if the wires were superconductors (zero resistance). But wires do have some small finite resistance so, in practice, there is a tiny potential difference between any two points on each conducting wire, correct? The presence of a nonzero (even if small) potential difference implies the presence of an electric field E=Delta_V/d between points separated by distance d.

This nonzero electric field E exists and is longitudinal both on the surface of the wire and inside the wire, correct?

If the wires were superconducting (truly zero resistance), a DC current would still flow in them. The current is determined and limited by the 2Ohm resistor. The wires now have a nonzero current but zero resistance. From Ohm's law J=sigma*E, the electric field is zero in this case which means that there is no effort (and no energy loss) in moving the charges inside the wires to produce the current. The wires would be equipotential conductor (situation different from the equipotential conductors in electrostatics where there is no net moving charge inside the conductor volumes and the E field is normal to the surface)

Does the same happen in AC circuits, i.e. there is a small but nonzero potential difference between any pairs of points on the same conductor, if the voltage source was time-varying? Clearly, there is a potential difference between the different conducting wires since they are connected to the two different terminals of the voltage source...

Thanks,

fog37