Difference between Resistance/Conductance and Conductors

Thread Starter

TransistorFun1986

Joined Nov 26, 2017
9
This is a question I've wondered for a while.

It seems very weird to me that in order to create a current and have conduction, you need to actually put a resistance/conductance in a circuit. That is, a perfect conductor itself will not carry either a (finite) current or a voltage.

From a engineering point of view this sounds wrong and non sense. From a physics point of view, this is because in a perfect conductor charges will immediately distribute themselves in order to cancel out any voltages created, therefore voltages cannot exist unless a resistance to charge movement is inserted.

The case of currents however seems more complicated... A voltage applied to a perfect conductor from end to end, would create an infinite current rather than a finite one. But what is correct to say? That there is no voltage, or that the current is infinite ? The question is, a perfect conductor will not carry a current because any voltages applied to its ends will instantly cancel out, or because the current will be infinite?

Anyways it sounds weird to me that in order to have a current, one needs to add a resistance to the circuit. It doesnt sound as weird if the resistance is seen as a conductance, but then a perfect conductor is the best conductance.

What happens at the atomic level when a voltage is applied to a perfect conductor?
 

kubeek

Joined Sep 20, 2005
5,724
... It seems very weird to me that in order to create a current and have conduction, you need to actually put a resistance/conductance in a circuit. That is, a perfect conductor itself will not carry either a (finite) current or a voltage.
No.

The case of currents however seems more complicated... A voltage applied to a perfect conductor from end to end, would create an infinite current rather than a finite one. But what is correct to say? That there is no voltage, or that the current is infinite ?
If you try to apply voltage, then the current would be infinite. However that is the theory, and in reality there is no perfect voltage source (one with zero internal resistance), so this can actually never happen.

The question is, a perfect conductor will not carry a current because any voltages applied to its ends will instantly cancel out, or because the current will be infinite?
Anyways it sounds weird to me that in order to have a current, one needs to add a resistance to the circuit. It doesnt sound as weird if the resistance is seen as a conductance, but then a perfect conductor is the best conductance.
Again not true, a perfect conductor will perfectly carry any current and will have no voltage drop from one end to the other, see superconductors in MRI machine for example. You can have current flowing through a perfect conductor, it just acts as a perfect piece of wire. There voltage drop across the wire is not required in order to have current, the current can be maintained by electric potentials that are outside said perfect conductor.

Say you have a 1V battery and to it you attach a 1 ohm resistor and a piece of superconductor in series. There will be 1A flowing and there will be no voltage difference between one end of the superconductor to the other.
 

AnalogKid

Joined Aug 1, 2013
8,443
It is correct to say that if a perfect (zero ohm) conductor is applied across a perfect (infinite current capability, zero ohm output impedance) voltage source as a dead short, the conducted current will in fact be infinite.

ak
 

nsaspook

Joined Aug 27, 2009
7,282
A Superconductor has properties beyond a PEC. The most obvious is the magnetic field in the conductor from the current. A perfect conductor would just "freeze" the field stopping any changes (how to get the original stable field is another question), but in an ideal type I superconductor the field is always zero inside (expelled due to quantum effects, not electromagnetic) the conductor so you can inject current with a current source at a heated point in the loop and then "close the loop".
 

GopherT

Joined Nov 23, 2012
8,012
No part or voltage source is perfect. Plug a big enough load into your wall and the voltage will drop.

In the image below, the one ohm resistor should be replaced by the measured or calculated resistance in your battery, conductor or any other part.

Now, pick real values for real parts, real conductors, real voltage sources and you'll see that nothing is infinite.

CD537516-4B7A-4CB6-8EF5-3259487C2E12.jpeg
 

Thread Starter

TransistorFun1986

Joined Nov 26, 2017
9
No.

If you try to apply voltage, then the current would be infinite. However that is the theory, and in reality there is no perfect voltage source (one with zero internal resistance), so this can actually never happen.

Again not true, a perfect conductor will perfectly carry any current and will have no voltage drop from one end to the other, see superconductors in MRI machine for example. You can have current flowing through a perfect conductor, it just acts as a perfect piece of wire. There voltage drop across the wire is not required in order to have current, the current can be maintained by electric potentials that are outside said perfect conductor.

Say you have a 1V battery and to it you attach a 1 ohm resistor and a piece of superconductor in series. There will be 1A flowing and there will be no voltage difference between one end of the superconductor to the other.

I don't know what you said "No" and "Again not true" for as you didn't specify it.

I understand that a perfect conductor used in series with a resistance will carry a finite current. The question is a perfect conductor in series with a perfect voltage source will either carry an infinite current, or will cancel out any voltages applied and carry no current at all.
 

Thread Starter

TransistorFun1986

Joined Nov 26, 2017
9
It is correct to say that if a perfect (zero ohm) conductor is applied across a perfect (infinite current capability, zero ohm output impedance) voltage source as a dead short, the conducted current will in fact be infinite.

ak

Are you sure it will carry an infinite current? Or would the voltage applied to its ends just cancel out because it is a perfect conductor? I've watched lectures with Walter lewin where he says there is no current or voltage across a perfect conductor.
 

Thread Starter

TransistorFun1986

Joined Nov 26, 2017
9
No part or voltage source is perfect. Plug a big enough load into your wall and the voltage will drop.

In the image below, the one ohm resistor should be replaced by the measured or calculated resistance in your battery, conductor or any other part.

Now, pick real values for real parts, real conductors, real voltage sources and you'll see that nothing is infinite.

View attachment 140171

I understand that. What I want to know if whether a current exists in a perfect conductor + perfect voltage source series circuit ?
 

Thread Starter

TransistorFun1986

Joined Nov 26, 2017
9
If you apply a perfect voltage source to a perfect conductor, both the voltage and the current will be undefined. There is no voltage across a perfect conductor, and the current will be infinite. Why? Because With a perfect conductor, any voltage no matter how small will create an infinite current. So a finite current only happens if you apply a voltage of exactly zero (in theory). It's like dividing 0 by 0: it can be anything. From Ohm's law: V = IR so if V = 0, and R = 0, then I can be anything. R = 0 corresponds to a perfect conductor. So if V is finite and R = 0, then the current is infinite. So the answer is, any voltage applied to a perfect conductor will create an infinite current. What voltage would you measure across it? 0.
 

nsaspook

Joined Aug 27, 2009
7,282
http://www.physics.princeton.edu/~mcdonald/examples/perfect.pdf
In a broader vision of (quantum) electrodynamics, where “initial” conditions can include nonzero energy, the interior magnetic field of a perfect conductor can be nonzero, but time-independent, in the rest frame of the conductor.

Feynman took a stronger stance [28]: ...it is not possible to understand the magnetic effects of materials in any honest way from the point of view of classical physics. Such magnetic effects are a completely quantum-mechanical phenomenon. It is, however, possible to make some phoney classical arguments and to get some idea of what is going on.
 

neonstrobe

Joined May 15, 2009
81
The problem you mentioned is the 0/0 situation. For a finite voltage and zero impedance the current will be infinite, which physics (and maths) does not allow for. It won't matter what the voltage actually is. No meter is going to survive measuring that much current!
 
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