Current law explained

Question

Kirchhoff's Current Law (KCL) is experimentally proven but what exactly happens?. I have made a model by taking the drude model and adding the interactions between the electrons and the reason why current is same comes from this:

As electrons pass through a resistor they bounce back and forth, creating a potential which doesn't allow the next electrons which follow to pass. Those electrons then bounce back and this effect is transmitted through the whole wire. But there is always progress. Well, my model doesn't work quite well for electrons which don't have something to repel them to go back. Is this correct?

I ask this because in every website I checked (including stack exchange), when someone asks why current is steady the answers are always "KCL" and nobody seems to understand why this is happening. I know that KCL is correct but I can't imagine and there is no answer at the internet on what happens inside the wire exactly so that is why I posted this question.

Please do not try to explain it with the wave function of an electron, it will get too complicated.

Answer 1

We don't need an atomic model to explain Kirchhoff's current law (KCL). The electron configuration in the atom, or the type of atom for that matter, has no influence on KCL.

Such factors may influence the amount of current and the resistance and nanoscopic behaviour - but it doesn't influence the fact that all charge entering must also be leaving every second at any point in a steady circuit. All we need to consider to intuitively accept that fact is what steady current actually means.

Because, KCL only applies for steady currents.

We call a current steady when it is constant and unchanging over time.

At any point in such a steady (constant-current) circuit, if, say, 10 charges enter every second, then also 10 charges must leave that point every second. Otherwise, charge would accumulate there. If charge accumulated there, then the accumulating electric field would grow and grow and soon start to prevent further charges from arriving. This would slow down the current.

But if the current slowed down, we wouldn't call it steady.

Since this doesn't happen (in a steady circuit, current is constant), charge accumulation cannot be taking place. If charge is not accumulating anywhere, then everywhere, all that is entering must also be leaving any section or point in the circuit. And this is the point of KCL.

In non-steady circuits, such as a circuit with a capacitor that is being charged (charge would then be accumulating at the capacitor plate), KCL doesn't apply.

Answer 2

what happens inside the wire exactly?

There are electrons moving. They are moving very fast in random directions (Fermi velocity, in the order of 1000s of kilometers per second) and, in a complete electric circuit, on average in one direction (rather slowly, the so called "drift velocity" is well below millimeters per second for reasonable currents).

Since electrons are not created or destroyed in electric circuits, every electron that flows into a node of a network absolutely must leave it. There is no accumulation or release of accumulated charges because Kirchhoff's Laws per definition apply to steady currents only

The algebraic sum of currents in a network of conductors meeting at a point is zero.

So KCL is a direct consequence of a) steady current and b) conservation of electrons.