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If $R= 0$ , $V= 0$ and $I=$ $max$ (i.e. charges are flowing at a huge rate), but when there is no potential difference applied to a circuit, charges don't flow. That means huge current flows when there is no resistance, consequently, the potential difference is $0$ but no current flows if no cell is added to the circuit i.e. the potential difference is $0$ again. How to explain this contradiction?

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  • $\begingroup$ Unless you are working with superconductors, the resistance of a wire might be small but it is never really 0. We might approximate it as 0 when there are other devices in a circuit that limit the current. If there are no other devices, then you shouldn't try to use that approximation. $\endgroup$
    – The Photon
    Nov 22 '21 at 16:43
  • $\begingroup$ There have been many questions on this topic on this site (and on EE.SE) before. Please search and review what's been asked before, before asking a new question. $\endgroup$
    – The Photon
    Nov 22 '21 at 16:44
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    $\begingroup$ Does this answer your question? Ideal wire and resistance $\endgroup$
    – The Photon
    Nov 22 '21 at 16:46
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    $\begingroup$ Or maybe this? Voltage drop along an idealized resistance-free wire in a circuit? $\endgroup$
    – The Photon
    Nov 22 '21 at 16:50
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when there is no potential difference applied to a circuit, charges don't flow

This is not correct in general. This statement is valid only for a device with non-zero resistance. For an inductor, a capacitor, and a zero-resistance conductor it is not correct, charges can flow even with no potential difference.

For a capacitor current can flow with no voltage as long as the rate of change of the voltage is non-zero. For an inductor current can flow with no voltage as long as the rate of change of the current is zero. For a perfect conductor any current can flow with zero voltage.

So there is no contradiction. Ohm’s law is not a universal law. It is a specific rule that describes a small subset of all electrical devices.

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