# Is Current in Superconductors Truly Infinite?

• Rakib771
In summary, a superconductor is a material that has zero resistance, which implies that according to I=nAvq , v must be infinite too. However, this does not always hold true, and when the current exceeds the critical current density, the material will revert to conventional resistive behavior.
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.

Delta2
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.

cabraham, phyzguy, vanhees71 and 1 other person
Rakib771 said:
...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.

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

Rakib771, Lord Jestocost and Delta2
Rakib771 said:
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.

Rakib771 said:
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##.

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Rakib771, Delta2 and vanhees71
Dale said:
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.

Dale
Baluncore said:
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.

Rakib771 said:
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.

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vanhees71 and Dale
Rakib771 said:
Can God create a stone so big he can't lift it?

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.

Delta2

## 1. What is a superconductor?

A superconductor is a material that has the ability to conduct electricity with zero resistance and without any energy loss. This means that current can flow through a superconductor without any loss of energy, making it an extremely efficient conductor.

## 2. What is the critical temperature of a superconductor?

The critical temperature of a superconductor is the temperature at which it loses its superconducting properties and starts to exhibit resistance. This temperature varies depending on the material and can range from a few degrees above absolute zero to above room temperature.

## 3. How does current flow in a superconductor?

Current in a superconductor flows through a phenomenon called Cooper pairs, which are pairs of electrons that move together without resistance. These Cooper pairs are able to move through the material without any collisions, resulting in zero resistance and perfect conductivity.

## 4. What are the practical applications of superconductors?

Superconductors have many practical applications, including in medical imaging devices, particle accelerators, and high-speed trains. They are also being researched for use in energy-efficient power transmission and storage systems.

## 5. What are the challenges in using superconductors?

One of the main challenges in using superconductors is the need for extremely low temperatures in order to maintain their superconducting properties. This requires expensive and complex cooling systems. Additionally, the materials used in superconductors can be expensive and difficult to manufacture in large quantities.

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