☐ How do electrons (or holes) know which branch to go through? 🤔

Something that has always baffled me about electricity is how electrons (or electron-holes/charge-carriers) know which branch in a circuit to go through.

At a low-level, we picture conductors like wires as being similar to tubes or pipes and electrons as water, or according to many diagrams, as little balls. Using various laws (e.g., Kirchhoff’s circuit law), we can calculate different electrical aspects such as voltage, current, resistance, etc. through the circuit, which tells us how much charge (and even how many electrons) flow through any part of the circuit, but that begs the question of how the electrons know which part of the circuit they need to go through.

For example, if there’s a junction in the circuit with a resistor one path and another resistor with a higher resistance on the other path, the one with the lower resistance will have more electrons flowing through it, but how do the electrons know which path they should go through before they go down a path?

In this case, it’s sort of easy to imagine that the higher resistance causes them to bunch up like a traffic-jam, which makes it harder for them to zip through, so more go through the other side, but this analogy doesn’t always work. The same question applies to other electrical properties and even more complex circuit schematics. For example, what about a circuit in which the aforementioned parallel resistors are followed in serial with the opposite resistor? The two paths are now equal in resistance, but he traffic-jam analogy doesn’t apply. How do the electrons still work out ahead of the first junction that which path to go down so that they’re all equal at the end?

I can’t help but think that the answer to this question is another example of the mess of the quantum world. That maybe it’s because the electrons exist at all points in the circuit and only manifest after reaching the goal, then the path to take goes back, something like the quantum-eraser. 🤔

One thought to “☐ How do electrons (or holes) know which branch to go through? 🤔”

  1. Hi! I randomly found your website from StackExchange, and although I ended up overstaying much longer than I would dare to admit, I read many interesting things here, so I thought that I’d give some back in what may be the only question I am able to help with.

    At first I was going to go on about how electrons also behave as waves because imagining the circulation of a continuum of electronic density clouds instead of particles may make it more easy to get the feeling of what’s going on. But after giving it a second thought, I think that sticking to the particle model will make it easier to understand through analogies.

    The key is understanding that in this situation electrons act as a sort of fluid. If you think about it, every typical fluid (water, air…) is made up of atoms (which can also be modeled as little balls) which are just not very attached to each other (nor to anything else), so they can flow within whatever space they are confined to. Electrons (the ones in the conduction band) in a conductor are like that; they actually repel each other and they are not too attached to any individual atom, so they can just roam around through the conductor. I think that rather than water, an example with air may be easier to explain.
    (bear in mind that I will make many oversimplifications along the way; what’s important in the end is just the main effect)

    Imagine a U-shaped corridor with a door at each end. If you open both doors and place a fan blowing air in in one door and a fan blowing air out in the other door, you will create an air current all along the corridor, even in the places which are not in line with any of the fans. This happens because, by pushing atoms in or out, the fans create a difference in the density (and pressure) of the air along the corridor (the outward fan reduces the density at the “end” and the inward fan increases the density at the “beginning”), and the atoms will flow from the places with higher density to the places with lower density. As atoms move, they will also locally (and gradually) change the density along the corridor, until some sort of equilibrium is reached where the density decreases linearly as you move through the corridor from the inward fan until the outward fan. Because every position along the corridor has lower density than the previous position, the air will keep flowing throughout the whole corridor, as long as the fans are on.
    If you plug a battery (or any device capable of inducing a difference in electric potential) into a circuit, the – side will be pushing electrons into the circuit (locally increasing the electronic density in that region of the circuit), and the + side will be removing them from the circuit (locally reducing the electronic density), so electrons in that circuit will more or less behave like the gas atoms in the corridor with the fans on, and after reaching equilibrium the electronic density will decrease progressively from the – side until the + side. You can picture it as every consecutive conducting atom along the wire having fewer electrons than the previous one. So the electrons in any part of the circuit will just go in the direction that looks less crowded (towards the + side). This is actually something which just happens statistically whenever you have a difference in density in a fluid. And in the case of electrons, the effect is bigger because electrons repel other electrons, so the more crowded direction actively repels them. So the electrons don’t know the parts of the circuit where you applied a potential difference; it’s just that on one neighbouring atom there are more conduction electrons than on the neighbouring atom in the opposite direction, so they go wherever it’s least crowded. You can also imagine that they are pushed by the other electrons, which are moving in the same direction (this is the part related to repulsion).
    If the path branches (ignoring differences in resistance), the same density-driven rule applies, so in the end both paths will have the same density difference, and each electron will randomly go through one or another.

    (Just in case: having lower electronic density near the + side does not mean that the charge flow itself is lower, since the mean speed of electrons is also lower when the electronic density is higher, because there are more collisions. Also, keep in mind that the differences in density can be minuscule and the effect on the overall flow still apply on a statistical level)

    Regarding resistors and more complex stuff, the issue with the jam analogy is that it’s a flawed one, because our roads have 2 to ~10 lanes, whereas the number of conduction electrons per unit length in a wire is many orders of magnitude higher, and, most importantly, because we tend to imagine traffic jams where all cars stop, and that does not happen with a resistor (unless its resistivity is infinitely high, which would be kind of pointless).
    I think that an air-related analogy may be more helpful in this case too.
    I am not sure if you have ever tried to dry your laundry indoors while opening the windows or turning on the AC or a fan. If you have and you tried to optimise your drying, you will have noticed that if you put many consecutive clothes in a line along the air flow’s direction (kind of along a single path), the air flow around them will be reduced, and your clothes will take longer to dry. This is because the clothes will create resistance along that path, so most of the air will instead flow along a different parallel path. If you instead distribute your clothes along all the likely parallel paths (let’s say, in front of the open window, but distributed along its whole width), the air flow around each of them will be larger than if you put them along a single path, and they will take shorter to dry (with the more crowded paths taking longer than the least crowded ones). This is analogous to a parallel circuit where all branches have similar amount of resistance, and the first case with all clothes in line is analogous to a parallel circuit where one branch has a much higher total resistance than the others, so the current (air flow) along it will be much lower. The main point is: even if there are varying degrees of resistance, in no case does the air flow stop completely. However, when one path is more blocked (i.e. has higher resistance) than the others, most of the air flow happens through the other paths. This is because the flow of the air through the more blocked path is slower, which means that the air density will be higher at its beginning, and since air tends to flow towards wherever the density is lower, part of the air which would have gone through the more blocked path deviates and goes through another path instead. And it’s easy to imagine how the air will be slower along a path with 2 consecutive t-shirts than if there’s only 1, so more (and bigger) clothes will mean more resistance > slower air flow > higher density at the beginning of the path > more air atoms deviating into other paths (“>” are arrows here).
    With electrons it’s kind of the same; each unit of resistance along a branch of the circuit means that the electronic density at the beginning of that branch (right after the junction) will be higher, so a part of the would-be incoming electrons will deviate into the other branches, provided that their own resistance (hence electronic density after the junction) is lower.

    To go back to the initial analogy and make it a bit more complete, you can imagine a circuit as a system of branching corridors, where each path is a corridor, with fans as voltage sources where the direction of the fans determines in which direction the air density (i.e. voltage, i.e. -electron density) is increased and in which direction it is reduced, and cloth hangers as resistive elements where they slow down the flow, increasing the air density (i.e. electronic density) in whatever direction the air comes from. And whenever the corridors branch, most of the air’s atoms will just go through the least crowded path.

    Okay, I guess that should do it. I feel like the explanation would have been several times easier (and more understandable) if I’d used drawings or something, but it is what it is. I hope this helped 😀

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