What IS the current in a superconductor measured as?

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happyjack27
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Post by happyjack27 »

resistance is not absolutely zero. e.g. the fact that its finite means it has an edge and just outside the edge is a non-superconductor and electrons can go there via e.g. quantum tunneling. 'cause its still only a finite energy barrier.

so you have non-zero resistance. the answer is you go from e.g. 1000 amps at 100 volts to 10000000 amps at 100 volts.

KitemanSA
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Post by KitemanSA »

I think I MAY be understanding your question now.
Given the circuit below, where the straight lines are all superconductors unless there is a resistor (/\/\) in the way. The center cross wire is also SC but is above the transition temperature so it has resistance. The current is your typical V=I*R1 equation and while the center cross wire has resistance, no current goes through it. However, if you cool it down, it becomes SC and the current stops flowing thru R1 and takes the easy path thru R2=0.
Nuff said?

Code: Select all

     <-I
+-----------+
|           |
|    R2     |
+---/\/\----+
|           |
+--||-/\/\--+
   V   R1

mdeminico
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Post by mdeminico »

KitemanSA wrote:I think I MAY be understanding your question now.
Given the circuit below, where the straight lines are all superconductors unless there is a resistor (/\/\) in the way. The center cross wire is also SC but is above the transition temperature so it has resistance. The current is your typical V=I*R1 equation and while the center cross wire has resistance, no current goes through it. However, if you cool it down, it becomes SC and the current stops flowing thru R1 and takes the easy path thru R2=0.
Nuff said?

Code: Select all

     <-I
+-----------+
|           |
|    R2     |
+---/\/\----+
|           |
+--||-/\/\--+
   V   R1
That would be an example of a system in question, yes. So, while it's above Tc, current flows through R1, and you have V=I*R1

As soon as it cools, the equation changes to V=I*R2, but what is R2? Some say it's not zero, because then V would also be 0, and I could be anything from -infinity to infinity.

D Tibbets
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Post by D Tibbets »

If Ohms Law doesn't strictly apply in DC superconductors, them things seem to work out (in my mind). So long as the resistance is close enough to zero that it doesn't make any measurable difference, things work. Inductance would always be present while the superconductor is being charged from a very well filtered DC source, but so long as the charging rate was slow enough, the heat generated would be easily managed. What I wonder is how much voltage is actually present. It might be ALMOST infinitely small, but there has to be some for the electrons to have some net direction of flow. This is counter to some arguments I have heard in another thread that there is absolutely no voltage across a super conductor.

A side question is: what is the velocity of electrons in a superconducter? If they are fast enough for Relativity to have a significant effect, that might act as a bridge between Ohms Law and superconductor characteristics.
Then there is the interaction between the bulk superconductor and the surface of the superconductor. Perhaps the equivalent of a tiny voltage on the surface and convoluted physical interactions is what drives the current flow through the superconductor.

There is heated discussions about the physics of superconductors by knowledgeable people within another thread, so I doubt my basic physics level of understanding can shed much light on the situation.

Dan Tibbets
To error is human... and I'm very human.

KitemanSA
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Post by KitemanSA »

mdeminico wrote: That would be an example of a system in question, yes. So, while it's above Tc, current flows through R1, and you have V=I*R1.

As soon as it cools, the equation changes to V=I*R2, but what is R2? Some say it's not zero, because then V would also be 0, and I could be anything from -infinity to infinity.
It may be that R2 is not EXACTLY zero in which case the ΔV2 would be a very small positive number too and the I1 would reduce slowly with time (i.e., you'd have a very low frequency AC circuit!). But even if R2=0, the equation would still hold as ΔV2 would also be 0. No?

Aero
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Post by Aero »

From Wikipedia:
Experimental evidence points to a current lifetime of at least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature
http://en.wikipedia.org/wiki/Superconductivity
Resistance must be so close to zero as makes no difference.
Aero

happyjack27
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Post by happyjack27 »

an interesting not i realized though i've never heard it mentioned: if a superconductor has near zero resistance, then it will generate very little heat! meaning it can run at high currents for a long time and require only relatively little cooling.

Aero
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Post by Aero »

happyjack27 wrote:an interesting not i realized though i've never heard it mentioned: if a superconductor has near zero resistance, then it will generate very little heat! meaning it can run at high currents for a long time and require only relatively little cooling.
Super conducting MRI machines use about one liter of liquid helium per week for cooling. That is to reject ambient heat which penetrates the machine from the environment, not so much because the machine is generating heat internally, as I understand it.
Aero

mdeminico
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Post by mdeminico »

Perhaps the v=ir is a result of an effective resistance caused by the inductor itself?

So, there could be a moderate voltage, and a moderate current, relative to the amount of "resistance" created by the inductor? Or does an inductor not do this?

Aero
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Post by Aero »

From the Wikipedia article linked above:
The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage V across the sample. The resistance of the sample is given by Ohm's law as R = V/I. If the voltage is zero, this means that the resistance is zero and that the sample is in the superconducting state.
Also, from the same article:
The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics.
The article says that superconducting is a quantum mechanical phenomenon so to understand it properly, one must also understand quantum mechanics. I don't, so I'll stop here.
Aero

Will
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Post by Will »

D Tibbets wrote:If Ohms Law doesn't strictly apply in DC superconductors, them things seem to work out (in my mind). So long as the resistance is close enough to zero that it doesn't make any measurable difference, things work. Inductance would always be present while the superconductor is being charged from a very well filtered DC source, but so long as the charging rate was slow enough, the heat generated would be easily managed. What I wonder is how much voltage is actually present. It might be ALMOST infinitely small, but there has to be some for the electrons to have some net direction of flow. This is counter to some arguments I have heard in another thread that there is absolutely no voltage across a super conductor.
The "voltage" is provided by the inductively generated magnetic field - think about what happens when a superconductor is charged - the magnetic field establishment generates back EMF (i.e. a voltage across the superconductor). When the superconductor is discharged, the magnetic field is collapsing.

In a closed superconductor, the magnetic field can be thought of to be continuously collapsing - but since resistive losses are zero, it's exactly counter-balanced by the creation of a new magnetic field.

There are no "heat losses" in a superconductor, because there is no resistance. Also as far as I know, conventional superconductors don't present an energy barrier when connected to an ordinary circuit, but ballistic transport semiconductors do (carbon nanotubes - they superconduct electrons, but only electrons above a particular energy level can successfully enter the nanotubes to start with).
D Tibbets wrote:A side question is: what is the velocity of electrons in a superconducter? If they are fast enough for Relativity to have a significant effect, that might act as a bridge between Ohms Law and superconductor characteristics.
Then there is the interaction between the bulk superconductor and the surface of the superconductor. Perhaps the equivalent of a tiny voltage on the surface and convoluted physical interactions is what drives the current flow through the superconductor.
AFAIK electrons within a superconductor are not moving at relativistic velocities. Superconductors are governed by quantum mechanics - electrons within a superconductor are basically a wavefunction which extends through the entire length of the superconductor. This can be seen in Josephson junctions, where superconducting current tunnels from one superconductor to the next.

The very hand-wavy explanation of low-temperature superconductors is that when the temperature is sufficiently reduced in the right metals, lattice vibrations are canceled out and electrons become capable of forming Cooper pairs permanently (i.e. they run zero risk of being disrupted by a collision with an errant part of the crystal lattice acting under thermal vibrations). The pairs bend the lattice in front of them to advance, and essentially kick each other along.

The key element here is the lattice collisions (at this level of explanation) - resistance is electrons hitting the crystal lattice and converting their kinetic energy into lattice kinetic energy (i.e. lattice vibrations i.e. heat).

EDIT: I really want to stress though that this is super-simplified. Superconductivity is a very heavily investigated phenomenon, because we don't understand it particularly well, and is fundamentally a quantum mechanical phenomenon. BCS theory is however the generally accepted model for describing low temperature superconductors (high-temperature superconductors are some new type of thing entirely).

happyjack27
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Post by happyjack27 »

ah yes, on the point of magnetic fields, inductance and what not tend to work towards opposing changes in the magnetic field. so it would take work to create the field, and the it would take work to destroy it (or you could simply take out out of superconducting mode), and more generally it would take work to change it. but it would not take work to maintain it.

Stoney3K
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Post by Stoney3K »

happyjack27 wrote:ah yes, on the point of magnetic fields, inductance and what not tend to work towards opposing changes in the magnetic field. so it would take work to create the field, and the it would take work to destroy it (or you could simply take out out of superconducting mode), and more generally it would take work to change it. but it would not take work to maintain it.
So, in more lament's terms, a superconductor can be thought of as a flywheel in a friction-less environment?

If you induce a current into it, it'll just keep going forever unless you do something to take it out again (e.g. induce a current in the opposite direction).

That poses another question: How are you supposed to calculate the energy stored in a superconducting loop, when it has effectively zero resistance?
Because we can.

hanelyp
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Post by hanelyp »

Stoney3K wrote:That poses another question: How are you supposed to calculate the energy stored in a superconducting loop, when it has effectively zero resistance?
Inductance. Or equivalently the energy of the magnetic field produced by the current.

happyjack27
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Post by happyjack27 »

Stoney3K wrote: So, in more lament's terms, a superconductor can be thought of as a flywheel in a friction-less environment?

If you induce a current into it, it'll just keep going forever unless you do something to take it out again (e.g. induce a current in the opposite direction).
the term is layman (from brick layer? not sure of the etymology.) but layman's terms are usually thought to be an oversimplification, and on the contrary that is an excellent analogy! that is _exactly_ how it is, and a much better description than _i_ did!

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