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I'm struggling to understand the fundamental concepts of electricity, more specifically, the way in which it 'chooses' its optimal pathway.

I appreciate electricity will always choose the path of least resistance, but how does it know which route has least resistance? Does it attempt that, potentially sub-optimal, route first before deciding not to take it?

This question comes from a discussion on the effect of electricity on the body when hanging on a charged wire, as opposed to hanging on a charged wire whilst touching the ground. I can hang on the wire all day, safely, but the minute I touch the ground the electricity all of a sudden decides that that is the best route. Did it previously try this route?

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instead of thinking your body is empty and that a charged wire has to push electrons one by one through you and into the ground (blood is actually full of charge carriers), a better analogy would be a very long queue of pushy people.

if the entrance to the apple store doesn't open, it doesn't matter how hard the guy at the back pushes--nothing moves. touching your feet to the ground is analagous to opening that front door and allowing the whole queue to move at once, with the pushing (electromotive) force provided by the difference in electric potential between the charged wire and the ground. every electron leaving your foot is pushed and replaced by an electron entering you from the wire.

needless to say if you didnt touch your feet to the ground your entire body assumes the same potential as the wire--you become an extension to that wire, a long queue of impatient charge carriers waiting to burst through any available door. if the wire voltage is high enough you wont need to touch the ground--the high potential will strip electrons from air molecules--corona discharge from your protruding body parts will not be comfortable.

while we're on the subject, dont assume that footwear will always save you. the human body can also function as a capacitor (with your feet and the ground being the coupled conductors and your shoes being the dielectric material). alternating currents can flow through capacitors.

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Gregsan's and Kieran's answers are insightful analogies and the pushy electrons are certainly part of the answer.

There is another aspect to the "decision" process and that is the propagation of electromagnetic waves. There is a chapter in the second volume of the Feynman Lectures on Physics - I don't have it with me but the relevant section will be just after the Poynting theorem and energy flux is introduced - where Feynman discusses a simple DC circuit and what happens in detail when the switch is closed. This would be a good reference for you.

In a very real sense, energy is NOT being transferred through the wires, it is travelling through free space around the wires: the electrons in the wires feel the propagating field and are shifted accordingly, thus setting up the usual high conductivity boundary conditions which then guide the "probing" waves. Every change in a circuit begets waves propagating at the speed of light, which then "probe" the rest of the circuit and charge thus may or may not shift in response to the wave. So when you touch the ground, a wave propagates back towards the power source, and a complex sequence of scattered waves bouncing back and forth between you and other parts of the circuit as the new, lethal, steady state conditions take shape.

Transmission line theory is a good starting point to thinking along these lines by giving you simple wave solutions which let you thing about changes "telling" the rest of the circuit through a "notification" message propagated as a voltage/current wave which, together with the (theoretically infinite) sequence of scattered waves it begets, leads to the shift in steady state conditions.

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  • $\begingroup$ This is very good answer but it could benefit from some formatting. $\endgroup$
    – Alfred Centauri
    Commented Oct 10, 2013 at 23:13
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    $\begingroup$ Thanks Alfred for doing that. It was written rather hurriedly to try to take my mind off some turbulence in the plane I am riding in that is scaring the **** out of me. $\endgroup$
    – Selene Routley
    Commented Oct 10, 2013 at 23:30
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    $\begingroup$ Ho hum, I wish downvoters would say why. If you can see something I can't I'd like to know - as would many other readers. $\endgroup$
    – Selene Routley
    Commented Oct 11, 2013 at 8:53
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Suppose you have a "current" in a wire of one electron, and that there are two possible paths for the electron, each with a different resistance. Then the electron will go through one or the other with a 50% chance, regardless of the easiest path.

Now if you have a lot of electrons, they will also initially go through this random process. But after a very short time, the path with more resistance will be more "clogged up" with electrons and harder to get into. So the electrons from then on will take the easier path more. This process repeats until the two balance out. However it happens over a very short time scale.

In this sense, the properties of resistance and current are macroscopic, ie they only make sense with very big numbers and sufficiently long time scales.

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