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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.

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  • $\begingroup$ if there is no resistance there is no potential difference indeed along the wire. However, the cell maintains a potential difference. The reason we come to a paradox is because of your perfect assumptions. In reality the resistance of the wire would generate joule losses which will decrease the voltage at the cell over time. Once all the energy stored in the cell has been used there is no currents anymore. Then it only remains the voltage at the cell due to the electrochemical rest potential. So there is a potential difference on the wire but no electrons available to balance it. $\endgroup$ – Ronan Tarik Drevon Nov 25 '16 at 11:13
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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.

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  • $\begingroup$ @freecharlyThen doesn't that mean that a potential difference can exist across a zero resistance wire;provided the current is infinity $\endgroup$ – Deepak M S Nov 25 '16 at 17:14
  • $\begingroup$ @Deepakms - If you let the resistance go to zero the current will go to infinity, therefore in this way to consider it, yes. But this reasoning is purely mathematical because there exists no ideal cell with zero internal resistance. Therefore, the question has no relevance for any real cell and actually doesn't make much sense physically. $\endgroup$ – freecharly Nov 25 '16 at 17:36
  • $\begingroup$ @freecharlyThanks for the answer. However if in this case, I=infinity and R=0 then V=IR=0*infinity. Does it mean that 0*infinity=V $\endgroup$ – Deepak M S Nov 25 '16 at 17:53
  • $\begingroup$ @Deepakms - Yes, mathematically Ohms law is used. Therefore, when $R$ goes to zero, $I$ goes to infinity in such a way that $V=RI$ stays constant. $\endgroup$ – freecharly Nov 25 '16 at 18:00

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