Understanding the Logic Behind KCL: An Exploration

[YoshiMoshi]

Homework Statement

Ok so I remember learning KCL. Current is either entering or leaving the node. There's only two possible option. You can call entering the node positive or negative, you can call current exiting the node either positive or negative. As long as what you call entering the node not the same thing as what you call leaving the node.

Ok great. I never questioned that. But I want to know the real reason why. Yes I know this is "just how it is", "convention"...

There's only two options agreed. So it's like I either put money into the bank account or It take it out, or let it stay in there so maybe this is a bad analogy.

But I guess if it's either going in or out, but has multiple pathways to go in or out, than why do we associate with only two possible scenarios positive or negative?

Example, there's a four way intersection. There's a car "moving forward" into the intersection. I define a coordinate system at the center of the car so that the "moving forward" direction is positive X, moving in the opposite direction is negative X. The car enters the four way intersection and turns left, during this whole process the car continues to move forward. Meaning as it rotates to make the turn, the coordinate system rotates with it meaning it never went in "reverse". So we associate such movement as going in only one direction "forward" and not "reverse" at all.

Even if I defined a coordinate system at the middle of the intersection (node) than I have four possible directions from the origin to travel, or if it was grass field many at different angles with respect to a two axis system.

So what gives with current entering and leaving a node? Does it have to do with something along the lines of the charge entering the node, isn't necessarily the charge that went down path A to component Z, it could have gone down path B to component Y? Ok but as long as the current doesn't start going in the reverse direction back from were it came and the charge never goes in the reverse direction than why is it associated with the opposite direction.

Homework Equations

The Attempt at a Solution

I know by convention and so forth. Ok fine, but when I think of an analogy of car entering an intersection the relationship doesn't seem to hold. I never questions KCL while learning circuits. Just sort of the old this is the law don't question it it's correct. Learn all about circuits without knowing why it's the law or the truth.

 

[andrewkirk]

Rather than cars on a road, pipes containing water is an analogy that works better for KCL. Cars don't work well because the number of cars entering or leaving the intersection per second is very low, and the number of cars in the intersection can vary significantly, both in absolute terms and relative to the number of cars approaching the intersection. With current, if we think of it as a flow of electrons (there's on need to get into fields or quantum mechanics for this purpose) the number of electrons entering the node per second is enormous, and the ratio of electrons in the node to those approaching is pretty constant. That's the case with water too, where we replace electrons by water molecules.

In the water case, the number of molecules flowing in must be pretty close to the number flowing out because the junction/node fits a fixed number of molecules. The ones coming in push on those in the node, which push others in the node out into exit pipes. If flow is smooth, every connected pipe will have flow either in,to the node, out of it or neither, and all molecules go that way for that pipe. If flow is turbulent (and flow is always at least a little bit turbulent), each pipe will have some going in and others out, but one or the other will dominate, and it is the net flow to/from that pipe that matters. It doesn't matter what any individual molecule does.