How does voltage affect particles in current

[e.chaniotakis]

Dear Screwy,
I don't really get the point of your question!
In room temperature, when the fermi velocity is ~10^6m/s while the drift velocity ~1mm/s, the kinetic energy due to the electric field is negligible compared to the fermi energy.
What happens in the conductor is, to me, that the electrons gain collectively a small amount of velocity in the direction of the potential difference and that's what causes the current.
Now about the cooling part, zero degrees Kelvin cannot be reached (3rd law of thermodynamics), and as we approach it quantum behavior becomes prominent..- energy is not zero.
As you cool a conductor, resistivity drops . This can be translated as the fact that since the temperature drops, fermi speed drops and the collision rate drops two. Therefore there will be more 'time' for the electron to speed up due to the electric field. Therefore mean velocity increases and thus the current. Is that what you want?
Cheers

P.S: Here is an interesting link about quantum behaviour http://www.asu.edu/news/Science-2012-Ferry-45-6.pdf

 

[mfb]

So if we observe a conductor with no potential difference at its ends at 0 degrees Kelvin, electrons are not moving at all.

The Fermi distribution at 0K has many electrons with significant momentum - this can be interpreted as "movement", and it is nearly the same as for room temperature.

 

[Simon Bridge]

If only we adopted Steinmetz' suggestion of defining voltage by the electrostatic (he called it the dielectric) field around the conductor, then all of these misunderstandings would not exist.

That would only add yet another use of the word "voltage" to get confused over. ;)

The concept of particles hurts our understanding of electricity, it is much easier defined in fields and waves.

Restricting to a single simplified model can only hurt ... doesn't matter if it is particles, waves, or something more exotic. You use the model that best fits the situation. The kinds of electric circuits being thought about here are very special cases and models which work for other cases will be inefficient here and t'other way 'round too.

But I think you are basically correct: it is OPs insistence on imagining electricity a certain way that is producing the problems. The exploration so far looks a lot like adding epicycles ad infinitum rather than abandoning the model in favor of something easier to use, doesn't it?

 

[Screwy]

the electrons gain collectively a small amount of velocity in the direction of the potential difference and that's what causes the current

In average, right? Not each and every one of them. Most of the motion is brownian motion, but it is biased in the direction of the current, so when you sum up all the vectors of velocity all that remains is drift speed.

 

[sophiecentaur]

But I think you are basically correct: it is OPs insistence on imagining electricity a certain way that is producing the problems. The exploration so far looks a lot like adding epicycles ad infinitum rather than abandoning the model in favor of something easier to use, doesn't it?

Nicely put. There is a terrible temptation to hang on, to the bitter end, with a familiar sounding model rather than make a leap to embrace a new one.

 

[e.chaniotakis]

Dear Screwy,
From what I can understand, all particles gain a more or less net drift velocity. However, the statistical nature of fermi motion smears the effect . When you speak of large numbers of particles, the fermi momenta sort of cancel out and what remains is the drift velocity.

 

[sophiecentaur]

I just hope the message gets across that, apart from an academic exercise, the calculation of electron drift velocity is pretty much irrelevant. It just takes one in the direction of not understanding rather than 'understanding' more. The net change in KE is just not an appreciable fraction of the energy transferred from power source to the load.

 

[e.chaniotakis]

Dear Sophiecentaur,
if you have read my post thoroughly, you will see that I have said:
"each electron gains kinetic energy within one mean free path due to the increase in the applied voltage and this results in increase in the current."
I hope that the term mean free path is clearly stated.
The calculation I have provided seems to provide a satisfactory explanation to the phenomenon (why current increases when we increase voltage). Of course, for everything that was not clear I will be more than happy to help.
Cheers

 

[sophiecentaur]

OK
Taking your model further, you have electrons with KE, which they lose on impact, each time. That is a loss mechanism / resistance. How would you take that model with you into superconductivity, in which there is no loss mechanism? The charges can be considered as moving but, unless you allow them an infinite free path, they have to be colliding with the lattice. Does that not make my point about the unsuitability of such a classical model in that context? The sums give you an answer, granted, but how relevant is it?

 

[e.chaniotakis]

I think that it is wrong to take superconductivity as a low temperature extension of conductivity. Isn't this what you suggest?
Let me remind you that materials such as copper, gold etc which are very good conductors cannot become superconductors no matter how much they are cooled.On the contrary, one of the best superconductors (YBa2Cu3O7) is an insulator at room temperatures!
Therefore it is mistaken to take a model standing for conductivity and move it to superconductivity.
In the latter, you deal with the creation of Cooper pairs. Meaning that if you have a couple of electrons moving in a positive ion lattice, the first one attracts the ions in its passage and the second is attracted by the ions. This way the electrons stick together . The two electron system behaves as a boson with zero spin,therefore no Fermi-Dirac statistics apply anymore. The two electrons move somehow ''resonantly'' (I am not sure if the wording is correct). This bunched behaviour, negates the effects of electrical resistivity met in normal conductors

 

[sophiecentaur]

@e.chaniotakis
In the solid state, electrons seem to behave like gas molecules only at a superficial level. For that reason, it worries me when people want to attribute the same sort of physical characteristics to them and expect the model to work. I am not convinced either way, actually and I am only being cautious. It has to be true, though, that many people approach these sorts of questions with a determination to have a 'mechanical' interpretation. I can see this is not true in your case, though.

 

[e.chaniotakis]

I think I understand your point.
I am mainly influenced by Einstein's work, who actually 'lived' with approximations when he described various phenomena. Take for example his work on specific heats. His model was as crude as it could be . He assumed that the solid consists of N independent oscillators which are all set to motion. This way he figured a formula for the specific heat of a solid which is correct in certain circumstances. Of course it is Drude who took it upon him to do the accurate theory. However, the beauty of Einstein's work was that with a very simple assumption produced results that can be checked experimentally.
This way of doing physics, conceptually yet not criminally, has never been taught to us in the university. Once I found it out, I have tried to understand it the best way possible. That's the spirit of my approach.

 

[Naty1]

One rough analogy of current flow is to consider a marble, for example, rolling down a long flight of stairs...it tends to reach a constant velocity of fall as the accelerating effects of gravity are canceled by the loss of energy via collisions with the stair treads.

Contrast this with near free motion of a marble dropped from a height in a vacuum...gravity will accelerate the marble during it's fall...
Or if in air, collisions with air molecules will also cause such initial 'free fall' to reach a terminal velocity, a steady rate of fall, due to collisions with air molecules...

 

[Naty1]

Also note that the heating loss in a given conductor is P = I²R = E²/R
where R is the resistance of the conductor...so as voltage or current flow increases so do the 'collision losses'...but of course in a typical circuit the conductor resistance R is small compared with the load resistance so power to the load definitely increases with additional voltage.

And this is analogous with heating losses in a battery either being discharged or charged more heavily...the battery gets warmer from internal resistance heating as current flow increases.

 

[Simon Bridge]

Nicely put. There is a terrible temptation to hang on, to the bitter end, with a familiar sounding model rather than make a leap to embrace a new one.

I don't think we are going to convince anybody - the core question seems to have been answered. Let them have their crutches, they'll learn they don't need them sooner or later as they advance in their studies.

 

[Screwy]

I agree.

People who have participated in this thread have mostly taken one of tho sides:

The easy-going party has procured the analogies and ideas which helped me form an image of a process that I am content with at the moment. This was the purpose of my question in the first place.

The other party, the cautious one, has brought to my attention the limitations of this approach. This is not at all any less of a revelation for me, and it will be maybe even more important point for me to take away from this thread.

I just wanted to thank you all for helping me, hope to see you more around here at PF.

OP out!