# Resistance at absolute zero

I was wondering, since resistance decreases along with temperature for most metallic conductors (usually power function), in theory, if this conductor were to be at zero kelvin, would the resistance of this material also be precisely zero, or would it just be some extremely small value?
If it was zero ohms, then short circuiting an ideal voltage source with a wire in these conditions would create an infinite current, which i believe is physically impossible, and so we have yet another reason why absolute zero isn't achievable. However it doesn't rule it out theoretically.
Anyway, does anyone have any ideas on the matter?

phinds
Gold Member
I was wondering, since resistance decreases along with temperature for most metallic conductors (usually power function), in theory, if this conductor were to be at zero kelvin, would the resistance of this material also be precisely zero, or would it just be some extremely small value?
If it was zero ohms, then short circuiting an ideal voltage source with a wire in these conditions would create an infinite current, which i believe is physically impossible, and so we have yet another reason why absolute zero isn't achievable. However it doesn't rule it out theoretically.
Anyway, does anyone have any ideas on the matter?

Nothing gets to absolute zero, but when you get really close, it's my understanding that the resistance goes to zero because the mechanism that causes resistance goes away.

As for an idea power supply, there is no such thing so your statement is not meaningful.

I know those things are not possible, I was just speculating. There's no need to get heated.
Anyways thanks for replying. I took a little time to look more extensively and i found the following:
Even near absolute zero, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature.

But maybe you're right. What particular mechanism did you have in mind?

It is wrong to think that you will have an infinite current.
The wire could well have zero resistance (this is what superconductors are) but the wire will also have an inductance which (as far as I know) is not temperature dependant. The inductance determines the rate at which current will rise so the best you can say is that a wire with resistance = 0 but inductance = 10H (for the sake of argument) will be observed to have a current increasing at 1A/s when connected to
10V (e = Ldi/dt)

phinds
Gold Member
Even near absolute zero, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature.

Yes, that's correct. I SHOULD have said superconductors, not just any material.

To my considerably surprize, when I looked at superconductors briefly last year, I found that two of the best conductors I am aware of, copper and gold, are NOT superconductors near zero degrees.

It is wrong to think that you will have an infinite current.
The wire could well have zero resistance (this is what superconductors are) but the wire will also have an inductance

I asked an ECE phd student I recently met about this, and he told me that it would only impede the current from reaching an infinite amount if it were alternating. Probably though, for direct current, capacitance (I guess normal wires have tiny capacitance just as inductance?) would kick in having the same effect.

Ok, thank you for the replies, you've all been very helpful.

phinds
Gold Member
I asked an ECE phd student I recently met about this, and he told me that it would only impede the current from reaching an infinite amount if it were alternating. Probably though, for direct current, capacitance (I guess normal wires have tiny capacitance just as inductance?) would kick in having the same effect.

Ok, thank you for the replies, you've all been very helpful.

Anyway, you can't SUPPLY infinite current, so whether or not it has that capacity is irrelevant from a practical point of view.

What would be the drift speed of this so called infinite current?

phinds
Gold Member
Anything you want it to be.

The statement

"If the current is infinite, the drift speed is X"

Is an absolutely true statement regardless of what X is because a false premise implies any result you like.

found that two of the best conductors I am aware of, copper and gold, are NOT superconductors near zero degrees.

You haven't heard of silver? :P

mfb
Mentor
Superconductors have a maximal current density - try to enforce more current, and they will stop to be superconducting. The resistance heats the superconductor, it can carry even less current, and heats more, and you get a nice quench.

While the current is not infinite, it can stay circulating for (nearly) an infinite time in a superconducting circuit.