Is Current in Superconductors Truly Infinite?

[Rakib771]

Hello! Recently, I became interested in superconductors. And I talked to professor in my uni. Here's my question, since superconductors have zero resistance by definition, so, in stable condition (after passing transient phase) the current should be infinite. Which implies that according to I=nAvq , v must be infinite too since n, A and q are finite constants. But infinite speed should not be possible (according to Relativity theory, I think!). So, my conclusion was that, in superconductors, the current would be a constant regardless of applied voltage which is constrained by the maximum velocity of electron only and the superconductor will show an apparent resistance according to Ohm's law. But, my professor said that the speed will be infinite too. Am I missing something?

PS: I know that superconductors are not used like that where you just connect a source to it directly. It's more like 'what would happen if we do that?'. Also, I know that in transient phase, the inductance will limit the current. I'm only considering stable condition.

 

[Baluncore]

A superconductor is always part of a greater circuit. It is never connected directly across a voltage source, so the current will not be infinite.

 

[Lord Jestocost]

...the current should be infinite. Which implies that according to I=nAvq , v must be infinite too since n, A and q are finite constants.

One cannot arbitrarily increase the current density in a superconductor. If the critical current density of a superconductor is exceeded, the electrons have sufficient kinetic energy to prevent the formation of Cooper pairs.

 

[vanhees71]

One should also note that in superconductors you don't have Ohm's Law, which only holds for currents in a normal conductor, where the motion of the conduction electrons (for a usual metal) is dissipative.

For a very good explanation of superconductivity from a modern point of view, see the Feynman Lectures vol. 3:

https://www.feynmanlectures.caltech.edu/III_21.html

 

[Dale]

since superconductors have zero resistance by definition, so, in stable condition (after passing transient phase) the current should be infinite

Superconductors don’t work that way. There is a critical current density above which the superconductor will suddenly revert to ordinary resistive behavior. As a result there is never any Ohmic voltage across a superconductor.

Which implies that according to I=nAvq , v must be infinite too since n, A and q are finite constants. But infinite speed should not be possible (according to Relativity theory, I think!).

You should calculate $v$ for the critical current density and compare it to $c$.

 

[Rakib771]

Superconductors don’t work that way. There is a critical current density above which the superconductor will suddenly revert to ordinary resistive behavior. As a result there is never any Ohmic voltage across a superconductor.

You should calculate $v$ for the critical current density and compare it to $c$.

Thanks. That helps.

 

[Rakib771]

A superconductor is always part of a greater circuit. It is never connected directly across a voltage source, so the current will not be infinite.

I am aware that it cannot be directly connected to a voltage source. But I was asking about a hypothetical situation.

 

[f95toli]

I am aware that it cannot be directly connected to a voltage source. But I was asking about a hypothetical situation.

Firstly, as has already been mentioned above the current would be limited by the critical current density of the superconductor.
Secondly, superconductors have zero DC resistance, at higher frequencies the resistance (not just the impedance) is non-zero meaning if you e.g. apply a sharp voltage pulse you will never "see" zero resistance even if you somehow removed the inductance.

What would happen if you applied a pulse is that the circuit would "see" some finite impedance (from the "usual" reactance, the frequency dependent resistance of the superconductor as well as the kinetic inductance) while the voltage ramps up until the point where the current flowing through the superconductor exceeds the critical current' at which point it becomes normal.

Thirdly, in the vast majority of cases (*) you simply can't relate the current through a conductor to the "motion" of electrons, even in a "simple" bulk normal metal conductor the physics is way more complicated than that. This is true for normal metals and it is also true for the transport of Cooper pairs in superconductors.

(*) There are cases where we can engineer situations where it actually works, but this is very much an exception.

 

[Vanadium 50]

But I was asking about a hypothetical situation.

Can God create a stone so big he can't lift it?

 

[Baluncore]

Can God create a stone so big he can't lift it?

Yes. It is now called Earth and could only be lifted if there was somewhere for Her agent Archimedes, to place the fulcrum.