TITLE: How could an ideal conductor with 0 resistance conduct electricity?
QUESTION [2 upvotes]: A very simple circuit consist of a resistor, a battery, and some conducting wires connecting the resistor to the battery(assuming resistance of the conducting wire is $0$). It is always assumed that both the ends of the conducting wire, i.e. one connecting to battery's terminal and other connecting to the terminal of resistor, are at equal potential and hence the potential difference is zero.
If the potential difference is zero inside conducting wire, then it implies that electric field inside the conductor must be zero. If this is the case then why does an electron inside the conducting wire move, and why there is current flowing through the wire?
My Idea
If the electric field inside conducting wire is zero then it only means that electrons inside conducting wire are not accelerating but can move with a constant speed and since current is the rate of flow of charge per unit time, so it is possible for electric current to exist in the conductor.

REPLY [2 votes]: My Idea
If the electric field inside conducting wire is zero then it only
  means that electrons inside conducting wire are not accelerating but
  can move with a constant speed and since current is the rate of flow
  of charge per unit time, so it is possible for electric current to
  exist in the conductor.

Essentially, that is correct. I like the mechanical analogy of pushing a box on a surface with friction vs one without friction.  When pushing the box on a surface with friction I have to apply a force equal to the opposing kinetic friction force which makes the box move at constant velocity. I do work which is dissipated as friction heating. This is analogous to the force of an electric field needed to do work to overcome electrical resistance, resulting in resistance heating.
But if I then encounter an ideal frictionless surface (the ideal zero resistance conductor) in the same path as the surface with friction, I can release the box and it will continue at the same constant velocity it had on the surface with friction, but now without the need of a force and work to keep the box going.
The two situations taken together are analogous to the same current flowing in a series circuit comprised of a resistor and an ideal zero resistance conductor.
Hope this helps.