I know the question might sound slighly basic, but stay with me here.
Kirchoff's Current Law states that
"The algebraic sum of currents in a network of conductors meeting at a
point is zero."
But how do we know that no charge gets "stuck" in the junction? Usually, I see people justifying KCL by pointing to the law of conservation of charge, but that doesn't mean that those charges couldn't get more or less concentrated in a region of a circuit. I understand physically that the electrons would want to spread out as far as possible, so of course they physically shouldn't get stuck in a junction – but how do we know that happens every time, and can we prove it in the lumped element model?
Best Answer
It's a point, so no charge can get 'stuck' there because there is no place for it to get stuck in. This point has no capacitance, inductance, resistance or length, so any current that flows into it must instantly flow out again. You can pump a billion amps into it and it won't store any charge, create a magnetic field, drop voltage or radiate. And how do we know it must do this? Kirchhoff’s Current Law.
Of course in a real circuit this 'point' does not exist. Real wires have capacitance, inductance, and resistance, and they generate magnetic and electric fields and act as antennas. So some charge may be stored there, or the current might take some time to build up, and a voltage drop might occur which causes some current to take a different path. But modelling all the characteristics of every piece of wire in a circuit is usually unnecessary, especially at low frequencies where the 'ideal' model is close enough. If you need to model some of those real-world characteristics you can easily add them to the theoretical circuit as separate components - which also don't exist in reality.
The beauty of electronics is that we work with these 'ideal' components to design and build devices that look nothing like the theoretical circuit, but work just the same no matter how we arrange them physically. We even go to a lot of effort to produce components that are closer to the 'ideal' in order to make designing circuits easier. It's not about describing reality, but being able to easily create a complex mathematical model which can then be 'emulated' with real-word components.