# Is it correct to generalize Kirchoff's current law to areas?

I'm very new at learning electronics, and I came across KCL. I think I understand it, I've used it to solve problems, and it makes sense to me (it feels very much like conservation laws in mechanics, no current gets created so what comes in at a junction comes out)

Thinking about this analogy (KCL and other conservation laws), I was wondering if there's a generalized version that goes beyond junctions to whole sections of a circuit. It would look something like this: "draw any enclosed area on a circuit, which may contain other components. Look at every connection going across the boundary of this area. Add the currents on those (with different sign based on their direction) and you should get zero.

It intuitively makes sense to me and I feel it could help me analyse bigger circuits. But I'm not sure if this generalization is actually valid, or if there are any counterexamples?

• Call things their names, oftentimes it accelerates your learning tempo. Talking about a thing that you call 'junction', an electrical engineer would use a word 'node'. Your idea of 'any enclosed area on a circuit, which may contain other components' also has a name in circuit theory: supernode ( en.wikipedia.org/wiki/Supernode_(circuit) ). Feb 6 at 11:34
• Amazing, I like knowing the right names but I didn't. I was thinking of the word "region", after some of the answers, I read the wikipedia entry you point at and I find it hard to relate with what I was talking about. Feb 8 at 1:11
• All the KCL formulations nowadays use 'node' (der Knoten in German), how could you miss this word. The word 'junction' (Knotenpunkt) is also used in some tutorials, but in electronics 'junction' is a polyseme. It is mostly used to designate semiconductor junctions. To avoid ambiguity, use more focused tags with your questions. For example, you may want to tag this question of yours 'futuristicircuittheory', 'gptcircuittheory'. Or maybe you do not mean circuit-theoretical 'kirchhoffs-laws'. Gustav Kirchhoff is a polymath physicist, and multiple concepts are named 'Kirchhoff's laws'. Feb 9 at 1:10

That generally works for electrical networks, but only if you restrict yourself to DC and harmonically oscillating currents, and have no nonlinear elements in there. No antennas.

I wouldn't have called this a generalization to areas (because the schematics you see are just notations of what connects to what, and do not only physical area) but to sub-circuits, by the way.

There is a generalization to areas, for example simply the current running through a section of a piece of sheet metal, and you'll probably learn about it sooner or later. It's called Maxwell's Equations and it deals with the current densities, the voltage potentials, the electrical fields and the magnetic fields as well as material properties, to achieve that. Of course, that is much more complicated than what you're currently learning - in fact, what you're currently learning will be indispensable for practical applications and to begin to learn about these equations.

Your generalization works fine as long as you account for displacement current (current through capacitances). Of course those may flow perpendicular to a planar circuit, so you should really consider volumes rather than areas. The sum of the physical currents and displacement currents into a volume is zero.

If you are using KCL, you are implicitly promising to account for displacement current.