As we know, superconductors have zero resistance. How can we measure the zero resistance in a superconductor? Can you devise an experiment to measure the zero value of resistance?
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4 Answers
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You can take a superconducting magnet and set it up to run in persistent mode. Here, you have a current running around and around in a loop of superconductor with no external source. If the current indeed persists (based on weak measurements of the magnetic field), then the resistance must be zero (or at least quite low, depending on the uncertainty).
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You take a real resistor with small resistance, measure the current, then you put your superconductor in series with it. If it's really superconducting, the current stays the same.
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5$\begingroup$ Or use a bridge for better accuracy, but absolutely. $\endgroup$ Jul 14, 2021 at 16:33
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3$\begingroup$ I think the real question is if you can ever measure a zero value for a variable is defined on a real valued interval. $\endgroup$ Jul 15, 2021 at 9:45
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$\begingroup$ @user000001 You can do it as well as you can measure anything precisely accurately. $\endgroup$– BarmarJul 15, 2021 at 14:18
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$\begingroup$ @Barmar: That's true for the absolute error, but not for the relative error. $\endgroup$ Jul 15, 2021 at 14:42
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$\begingroup$ @JonCuster: Technically, the other answers are better because you cannot increase your precision over time with this method. $\endgroup$ Jul 17, 2021 at 6:35
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As the other answer point out, you can devise simple methods that show the resistance of a superconductor is zero within the limits of experimental error. The size of your experimental error will depend on the precision of your measuring instruments and the length of time over which you conduct your experiment. This Wikipedia article says
... currents injected in superconducting coils have persisted for more than 25 years (as of August 4, 2020) in superconducting gravimeters.
answered Jul 15, 2021 at 10:16
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$\begingroup$ I think you should add some actual calculation based on your quote to show exactly how close to zero the resistance must be, in order to have (say) half-life of more than 25 years. $\endgroup$ Jul 17, 2021 at 6:33
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Note that often, superconductivity is established not by directly measuring resistance, but by the Meissner Effect: "the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. This expulsion will repel a nearby magnet."
