A question about an electron’s movement in a DC circuit

[Tiger]

I talked only about the wire and the electrons in it, not about the ions. For electrolytes of course you have both ions and electrons in the solution moving. The qualitative theory a la Drude is not so much different. No matter whether the voltage is low or high all these charge carriers move but the higher the voltage the larger the drift velocities get and thus also the larger the current gets.

Thanks. Vanhees71. I got the poit now. The higher the voltage, the faster the electrons move. Thank you

 

[vanhees71]

I have to agree with you basically BUT you are looking at this from the point of view of someone who already knows the whole (or most of the) picture. Imo it would be a disaster to try to teach the subject in this way. Far too many balls in the air at once for a newbie.
I do hate the water analogy but it is only at the other extreme to your 'full treatment all at once".

And you have to ask yourself what you actually mean by the word "adequate". Water is "adequate' for many purposes but "adequate" would need QM or better for some others.

You can't do it all in one pass and V=IR is a pretty good formula that you can learn and it works for a vast number of problems.

Hm, but I find the way proposed in the above quoted website okish. It's of course not full Maxwell theory, which is out of reach at 7-10th grade, but at least it proposes to use a qualitative field picture rather than the water analogy (note that you can't do fulfledged hydrodynamics in high school either, it's even more complicated than Maxwell's equations since it's nonlinear). I think it's pretty intuitive to discuss that there's an electric field along the wire and conduction electrons moving quasifree (with friction) driven by this field to overcome the friction (in the stationary case), i.e., the naive Drude model. I'm not sure, whether it's treatable for AC (in the quasistationary limit) at high school, where you have a quasifree particle with friction with a sinusoidal driving force. Perhaps it's just feasible in the last grades, where they have some calculus at hand (but of course not complex exponential functions, which make the calculation simpler than the use of trig. functions needed for a purely real calculation).

 

[hutchphd]

It seems to me that part of the problem is the attempt to provide facile explanations in the first place. It is far worse to give a woefully incomplete and therefore necessarily incorrect explanation to a student: they will assume a depth of knowledge that is unwarranted and it may in fact stifle, for those so imbued, the urgent need to know. This requires discipline from both student and teacher.
Teaching half-truths without relentlessly identifying them as such is therefore to be avoided as a reckless enterprise. Education is demanding. In my (limited) experience the systems that have traditionally been best with this disciplined approach have been those associated with the military. Their production of technically competent people from often educationally deficient backgrounds is remarkable.

 

[sophiecentaur]

“Half truths” is a perjurative term. You may have forgotten how used kids are to being given and making good use of limited information. I’m sure we had a much more pragmatic than purist attitude to learning when at school.
My memories of teaching are that many of the “Yes sir but what does that really mean” questions were more used to disrupt the lesson when things were getting hard.

 

[sophiecentaur]

Thanks. Vanhees71. I got the poit now. The higher the voltage, the faster the electrons move. Thank you

But you must realize that a small increase in almost nothing (kinetic energy) is still almost nothing and an insignificant fraction of the energy transferred.
something to consider: how much of the energy that a cyclist transfers to the wheels is ‘carried’ by the KE of the links.

 

[Nugatory]

I got the poit now. The higher the voltage, the faster the electrons move. Thank you

But be careful here and reread @mitochan’s post #3 in this thread about drift velocities. It’s the drift velocity that’s increasing with the voltage, not the speed the electrons are moving at. (The drift velocity is, loosely speaking, the difference between the average speed when they’re heading one direction and when they’re heading the other direction as they bounce randomly around)

 

[Tiger]

But be careful here and reread @mitochan’s post #3 in this thread about drift velocities. It’s the drift velocity that’s increasing with the voltage, not the speed the electrons are moving at. (The drift velocity is, loosely speaking, the difference between the average speed when they’re heading one direction and when they’re heading the other direction as they bounce randomly around)

Yes. I got that. The velocity they randomly move around is very fast but the drift velocity as current is much lower，which is related to the voltage in the circuit. Thank you guys. Merry Christmas and Happy New Year.

 

[vanhees71]

But be careful here and reread @mitochan’s post #3 in this thread about drift velocities. It’s the drift velocity that’s increasing with the voltage, not the speed the electrons are moving at. (The drift velocity is, loosely speaking, the difference between the average speed when they’re heading one direction and when they’re heading the other direction as they bounce randomly around)

The drift velocity is the macroscopic velocity of the "electron fluid", i.e., it's a quantity averaged over macroscopically small but microscopically large "fluid elements", i.e., the thermal motion is averaged out.