It was my friend who asked me this question first. Suppose we have an ideal cell and a wire of resistance zero.Suppose we short circuit the cell using the wire(although we know ideal cells and zero resistance wires are not practically possible). Would there be a potential difference across the wire . I think it ought to be there ; but my friend points to me that no potential difference exist across a zero resistance wire. Please help me.
An ideal voltage source (cell) with voltage $V$ doesn't have an internal resistance. If you short circuit the cell with a wire of resistance R, according to Ohms law a current $I=V/R$ will flow and there will be a potential difference $V$ across the wire. If you let the resistance of the wire go to zero, $R->0$, then the current will go to infinity but the voltage drop stays the same.
The question is, however, rather artificial because there exists no ideal voltage source, a galvanic cell will always have an internal resistance.