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When a material is cooled to reach it's SC-state, how can there be current flow if $R$ = $0$? Also, would a SC required excessive energy to maintain it's temperature & the SC state?

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how can there be current flow if R = 0

Not sure what the problem might be here. Assuming an ideal ohmic conductor, we have that

$$V = I R$$

where $V$ is the voltage across the conductor and $I$ is the current through.

Thus, if $R = 0$, the voltage across the conductor must be zero for any (finite) $I$. That is to say, the current can be any value (in this idealized case) and satisfy the equation.

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  • $\begingroup$ Well in terms of operation, how can one apply a voltage to allow current to flow? It's very odd to imagine! If $R$ = $0$ how can can we apply a potential different to allow current to flow? $\endgroup$ – Pupil Oct 30 '16 at 23:11
  • $\begingroup$ @XCIX, one can change current via a time dependent magnetic field. $\endgroup$ – Alfred Centauri Oct 30 '16 at 23:19
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Applying a a potential difference is fine, but $R$ being zero, there would be enormous amounts of current generated for even small values of the potential difference. Charges should have accelerated forever.(since there is no resistance, right ?) However, that is not the case. Due to the accelerating charges inside the superconductor there is radiation loss, which prevents the rising of charge velocities. On removing the emf source now, the acceleration of the charges will disappear, and the current will keep flowing since there is no resistance.

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