Question

what is potential difference of current carrying two conductor

Answer 1

if the sizes of the conductors are different. We have V = q/C. The capacitance depends upon the dimensions of the conductor. If the two conductors are of different shapes and sizes, they will be charged to different potentials even if they are given the same charge.

Answer 2

potential difference between two point in a circuit carrying some current as a work done to move a unit charge from one point to another.