Electric Field in simple circuit

[gayapatel]

Have attached a diagram of a sample circuit with emphasis placed on the valence and conduction band electrons of the copper wires. I know that there exists a voltage difference between the wires and can calculate current, etc. but now I'm trying to understand this circuit in terms of vector quantities (Electric Fields, Forces, Charge Separation, Drift Velocity).

Is my portrayal of the charge differences (charge density?) between the two conducting wires accurate? If so, since the current is equal in them, the drift velocity of the electrons in the High Potential Wire must be higher to compensate for the different in charge densities. Is this right?

Please bear with me, because I'm trying to get ILLUSTRATIVE INTUITION about circuits like this (without resorting to scalar quantities and vague/simplistic analogies of "voltage pressure"). Can anyone explain how the VOLTAGE difference is represented in circuits like this? I know the mathematics of voltage, electric field, electric force (Coloumb's law), etc. and I know how to do scalar calculations with these circuits, but the connection between these two entities gets blurred once I stare at a circuit like this.

Any help will be appreciated. Please no answers that talk about water hoses, cliffs, "pressure", or "energy drops." I am well aware of these analogies and ideas(mathematically)- what I am looking for now is a particle level illustrative answer/explanation.

Thanks to all.

 

[Xodar]

Hi,
I do not accept that your portrayal is accurate (or correct). [For that matter, I think you are overly dismissive of hydraulic analogies, which also have potential for explanation at the molecular level - whilst you are aware of the analogy you may not be "well" aware.]

If the two wires are going to have different charge densities, when did they get them? Presumably not before they were connected to the circuit. What would happen to this difference in charge density if the circuit was broken? Obviously your model is not consistent with a lumped parameter approach to circuits, but in what ways does it differ?

Do you have an "illustrative intuition" about magnetic field? How do you expect it will be different to electric field? Could the difference simply be that the things influenced by the electric field (electrons) are more mobile and consequently demonstrate flow characteristics. This would lead to possibly convincing explanations of semiconductors and non-conductors without having to resort to variations in charge density.

Hopefully this gives you a little more grist for your mill.

 

[willib]

since you have the same current flowing in your high potential wire as in your low potential wire , wouldn't the electrons in valance or conduction band be the same..?
bear in mind , you seem to be on a different ( higher ) level of thought than me.
i just never thought about it THAT much..

 

[barton]

I agree with your drawing at an intuitive level.

 

[jsgruszynski]

Well, the hydraulic model is not strictly correct but it has a very usable intuition as long as you don't try to take it too far. The more math you have, the less likely the problems. Then you can separate the component itself and remember how voltage and E-field are related.

The key thing about models (which every engineer should understand in every sinew of their being by the time they graduate with their BS or equivalent) is this:

A model is predictive tool that is only sufficiently accurate to get the job done effectively. All models are strictly wrong in any absolute sense - it's you responsibility to know when a model stops being accurate enough to be sufficiently correct for the purpose at hand.

This is why you always here words like "sufficiently" or "it depends" with engineering design - the problems are always underspecified and the model you use and the answer it gives depends on some of the up-front choices you make (which are based on a balance of not enough information and needing a real-live answer other than "It can't be done".

Being aware of the nature of models and their limits is key. One student I had somehow managed to get to his senior year without clearly understanding that small-signal models are just a convenient fiction. He thought there were perfectly real just because the textbook had cookbook formulas using them that he could remember. He was quite upset about and couldn't understand why his lab circuit designed for a gain of 100 didn't given him 100V with a 1V input and 12V power!

On the other end of the spectrum we had a joke in engineering school: "if you want really good laugh, ask a physicist to design a circuit for you. They'll start with Maxwell's equations and a month later..." (the implied punchline was that the same level of circuit design usually takes an EE a few minutes to accomplish and the circuit can be roughed in less than 60 seconds from experience).

Strictly speaking all lumped components like resistors, capacitors and inductors are purely fictional - they are useful models ("Lumped Equivalent Models") but not reality. It's all Maxwell's Equations at some point which is what you see when you get to microwave frequencies and the "Distributed Model". Except the fiction is sufficiently accurate and the expediency is necessary economically that lumped are used all the time as if they were real. We even manufacture components with those names. They are non-ideal, however, because the model they are based on is a fiction in a strict sense.

What did I use as an intuitive model when I was doing analog circuit design in undergrad and grad school? What I'd call a "mathy hydraulic model": sort the hydraulic model but really it was graph theory networks combined with linear algebra as the intuition. My adviser was a stickler for being able to write circuit analysis equations "by inspection" which means you visualize KVL or KCL and trace the loops or nodes writing Ohm's law for each component as an equation term. From that you can simply "look" at a circuit, visualize the equation and "know" what the input impedance is or the driving point impedance is or the Thevinen resistance is.

Most of EE involves multiple overlapping intuitive models, none of which are strictly physics correct. For radio systems I think of everything in terms of trig identities because that generally the easiest model to understand frequency, mixers, amplifier linearity, harmonic and intermodulation distortion. Dig a little deeper and it's circuit analysis with mathy hydraulic models. Dig a little deeper into a transistor stage and it's Taylor Expansions for large signal/small signal approximations. Dig a little deeper and it's particles with semi-classical quantum mechanical condensed matter physics and Maxwell's Equations. Dig a little deeper and it's second order stuff affecting reliability like hot carriers, traps and tunneling from mostly pure quantum mechanics. Trying to use a single model or a perfectly accurate model will only paralyze you. The human is not nearly smart enough to pull that off.

Again, from an pre-upper-division circuit analysis point of view, the hydraulic model isn't that bad. Lower division EE classes should build up the mathy aspects enough.