Ryan you are making no sense again. No diagram, no reference, so we have no idea what you are talking about.> so what's confusing me how really the dependent source voltage knows the voltage k at branch k?The source voltage cannot "know" anything. It is a battery (or something else) and has no knowledge of what is happening.> is the voltage k magically traverse to the dependent source voltage to supply?There's no magic here at all. Electronics works according to physical laws - Ohm's law and others. Two guys called Thévenin and Norton produced theorems a long time ago that assisted us to calculate voltages and currents in circuits. You HAVE to know these to understand electronics.If you don't know these subjects, yes it will seem like magic and you will confuse the hell out of yourself. I suggest you start at the beginning and work your way through these tutorials, they start right from basics so you may be able to skip over a bit depending on what you already know, but from your questions that does not seem to be a lot, so take care to learn everything in these tutorials. They are on our Electronics Tutorials website:https://www.electronics-tutorials.ws/dccircuits/dcp_1.htmlAt the end is a list of all the tutorials in the series, so you can just click to go onto the next one.The tutorials progress through Ohms law and Kirchoff's and Thévenin's theorems and how you can use them to analyse circuits. If you work through them in order and can grasp the contents of these tutorials, you will be well on your way to a good understanding of electronics.If you get stuck we will be pleased to help you, but please- Do not ask us about "Magic" and voltage sources "knowing" things. They just follow the laws of physics. Learn those laws.- Do not post questions like the above with no diagram and no reference, we will not have a clue what you are talking about.- If you are trying to work something out, show us what you have done so we may be able to see what you are doing wrong.I appreciate that your native language is probably not English and we can make allowances for that. However we cannot help you if you fire off questions like the above which make no sense. I have thought for a long time that you are a troll (just trying to annoy us) but Max is not sure so I am giving you the benefit of the doubt. Please prove us wrong.I repeat that a proper course in electronics will teach you subjects in order and stop you going off into areas where you have no idea what is going on (which seems to be the case above). Also, you will be able to ask questions as they occur to you and not wait for an answer. If you really cannot do that, work through the tutorials above and only move onto the next one if you have completely understood the one you are working on.Please, help us to help you, or you will never grasp electronics.