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My original question was in an effort to understand the electrical analogy to Markov chains, which is explained in Snell's article. There are some neat parallels that involve taking a Markov chain and considering the edge weights to be wire conductances. Unfortunately, after reading the article, I realize that they specifically say that their analogy is unrealistic.

So, how is electrical energy transmitted?

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Electron charge doesn't change. Are you talking about voltage drops? –  Mark Eichenlaub Nov 20 '10 at 11:42
I think I meant energy. (I'm not a physicist.) –  Neil G Nov 20 '10 at 11:49
The general problem is that electricity is much more than movement of electrons; it is much faster and AC current does not even need continuous wire to propagate. –  mbq Nov 20 '10 at 12:45
You can find a derivation of the Snell article here: math.dartmouth.edu/~doyle/docs/walks/walks.pdf - I'll try to write an answer, but I think the question could really benefit from a more detailed formulation as well. –  Thomas Themel Nov 20 '10 at 17:01
Your title doesn't seem to agree with your actual question; I'm not sure quite what you're asking here. Do electrons move faster when they have more energy? Simply, yes. –  Noldorin Nov 20 '10 at 21:19
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While the answer to the question in the title is simply 'yes', I assume that your question is: 'how do individual electrons move in electrical circuits'?

My answer to this question should explain that - it uses a simple but correct model for individual electrons versus macroscopic current. The relationship between macroscopic current and microscopic drift velocity is a linear relation. The same holds for the relationship between macroscopic resistance and microscopic resistance.

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I have changed my question as requested. –  Neil G Nov 24 '10 at 22:49
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uhm.. if i understood your doubt correctly, you want a macroscopic analogy of what happens with resistance and circuit.

If so, imagine a great concert in a stadium. hundred of thousand of people want to get in at the same time and they push so that, if materially possible, they would all entre the stadium at the same time (and this push is analog to the voltage drops i.e. the energy for unit of charge).

Now if you imagine the gate of the stadium, the wider the gate the higher the flux of people going in will be, i.e. the higher the current of people entering the stadium. The gate is analogous to the resistance: wider gate means lower resistance higher current (if the push of the crowd, i.e. the voltage drop, is kept constant).

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