Content-Type: text/shitpost

Last year someone asked an interesting but off-topic question on math stackexchange:

How voltage drop occurs in a resistor?

So I was getting confused over a thought, say I have a resistor and we have 10V source across it, now when electrons flow from negative end to the positive end they lose 10 joules of energy as they flow through the resistor, now with all the weird and crazy quantum stuff happening inside the wires how can we exactly predict how much energy an electron is going to lose that precise amount of energy when it passes through the resistor, can’t it do this - lose 5J of energy inside the resistor and continue with 5J energy left ?

Well, that is a good question, and I didn't really know the answer because I know very little about physics. But I thought about it and thought maybe I had the explanation, so I replied in the comments.

The question was later deleted, but I saw it again recently and thought that my explanation was worth preserving, so here it is:

I think the answer is going to look like this: if you throw a handful of fine sand, all the grains identical, off of a 100m cliff, some grains might fall straight down, some might be caught by the wind and whirled all about, but every single one will lose exactly !!100g/m!! joules per kilogram, where !!g!! is the acceleration of gravity in meters per second squared and !!m!! is the mass of a grain.

Three hours later:

Considering this more, I think the analogy is pretty good. The 10J loss (actually 10eV, but the principle is the same) is not a property of the resistor but of the power source. You can replace the resistor with any other resistor — bigger, smaller, different shape, different material, whatever — and the energy loss per electron will not change. The electrons lose 10eV each because the power source is a 10V source. This does not mean that it imparts 10eV to each electron; it means that the energy difference between its two terminals is 10eV per electron. The energy measurement is relative.

“Per electron” in the next-to-last sentence is wrong, but I think the rest of it is pretty good. In particular, my point about how the energy loss is not a property of the resistor. The energy loss is the same, regardless of the resistance; this is Kirchoff's voltage law. If you replace the resistor with one of lower resistance, the energy drop through it is still exactly the same (per electron), but the voltage source is able to push electrons through it at a greater rate; this is Ohm's law.