How do electrons “know” to share their voltage between two resistors?

Question

My physics teacher explained the difference between voltage and current using sandwiches. Each person gets a bag full of sandwiches when they pass through the battery. Current = the number of people passing through a particular point per unit time. Voltage = the (change in) number of sandwiches per person. In a parallel circuit the number of people (current) is divided between the two paths, but the number of sandwiches per person (voltage) remains the same. In a series circuit the number of people passing through a particular point remain the same, but they drop off a certain percentage of their sandwiches at every resistor. Therefore, there is a voltage drop that occurs between the points before and after every resistor.

This analogy naturally leads to the question: how do the electrons "know" that they are going to have to share their voltage between two resistors before they reach the second one? (In other words, not drop off all their sandwiches at the first resistor they find)

Answer 1

These laws are based on a circuit in equilibrium. If you made a circuit where you had +1 volt on the left, 1 ohm in the middle, and +2 volts on the right, and you started out with the resistor not under any voltage, electricity would start out moving towards the center of the resistor until it builds up a voltage of about 1.5 volts. (It would gradually change from 1 volt to two based on which source you're closer to.)

If you want to extend the sandwich analogy, imagine, for some reason, that the strength of people is proportional to their sandwiches. They also have no idea where they're going, and they push at random. And the number of sandwiches they drop is proportional to their speed.

In my circuit, at first people will be pushed by the people behind them, until they get to the center. At this point, the guys on the right have more sandwiches, so they shove the people on the left back, until you end up with just a group of people going from the right to the left. They're slowed down exactly enough to have one sandwich at the end, since if they went slower, they'd have more sandwiches than the guys they're pushing against, speeding them up. If they went faster, they'd have fewer, slowing them down.

The reason you always end up with everyone having the same number of sandwiches when they meet at a node is if they don't, the guys with more sandwiches push back on the guys with less, slowing them down, until they end up having the same number of sandwiches. It might be off for a little bit, but it will quickly enter an equilibrium.

Answer 2

The analogy used by the teacher is quite inappropiate, as pointed out by Georg. Do the electrons have to stop running when they are out of sandwiches? Or are they allowed to run on credit? Then: resistance is not part of the analogy (at least it is not mentioned) which is impossible because the analogy is about Ohms law: $V=IR$.

But then: also when using better models it is always a problem to think about individual electrons: how does one particular electron know that the voltage is lower at the other end of the loop? Individual electrons do not exist in QM, electrons are indistinguishable, they are a collective, so in your analogy, should all sandwhich eaters exist of some kind of clairvoyant species with a collective conscience?

Answer 3

Well, they don't know that actually. The picture you are familiar with is quite simplified. To explain the apparent emergent properties you need statistics and knowledge of microscopic physics. So what happens with that electron as it passes through the circuit? Well, let's start with resistors. Why is there any resistance at all? It's because electrons collide with the crystal lattice of the conductor and thereby lose energy (let me use this more familiar term instead of your sandwiches). How much? Well, it depends on precise realization of the collision. Some electrons scatter elastically (losing no energy at all, just changing direction of motion), some don't. But if you average this over all electrons (because there is so many of them in the material), you'll obtain the familiar Ohm's law for the heat losses.

Gaining of energy by electrons is pretty much same, but in reverse. There is a possibility that the electron will absorb a photon (which is a quantum of electromagnetic field) and this will boost it. Again, whether the collision is elastic or not doesn't matter. Once you average over all electrons and photons you'll be left with macroscopic effect of current produced by classical EM field.

Answer 4

Continuing Marek's reply, I will add that in electrical circuits the value of the current depends on the elements of the circuit: the voltage , the resistors summed when in series, summed inversely if in parallel. The whole defines the value of the current, and currents in the parallel parts, according to the electricity laws. The individual electrons participating in the current follow the flow, it is the current that "knows" where the resistances are .