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If an ideal superconductor was just left alone, with no potential difference, what would be the current flowing in it?

According to Ohm's Law, $V = IR$

Hence, if a superconductor of $0\Omega$ resistance was just placed with $0V$ across its ends, substituting these values into Ohm's Law, we get $0 = I0$.

In this condition what current would flow through the superconductor; would it be infinite or zero?

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Ohm’s law is vacuously true for a superconductor, regardless of the current going through it. You cannot use it to determine the current

You have to provide the current through some other means, like a current source, or putting it in series with a resistive circuit. Then whatever amount of current (up to the critical current) will conduct with no voltage.

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