Found this while searching an explanation for a homework, but I probably found the best way to properly getting introduced to the circuit part of electrical engineering, will definitely go through your videos! Thank you!
For those confused by the proof and its assumptions, reading the following may help. First step: we assume that there is a solution. By this I mean that we assume (very important) that there is a function that gives you R1 in terms of Ra, Rb and Rc only. We assume there is a function that gives you R2 in terms of Ra, Rb and Rc only. We do the same thing for R3; and, conversely, we assume there is a function that gives you Ra in terms of R1, R2 and R3 only; the same being true for Rb and Rc. This is no triviality, being these assumptions what gives sense to the whole proof. Now, if we assume all this, then whatever is true to one choice of voltages must be true to all choices of voltages. Let's clarify this: Let Vn be the voltage at the Y center. If we choose Vn3 = Vn, there is no current on R3 (Y circuit) and Rc is in parallel with Rb and Ra (no current going through node N3 on Delta circuit). By this you derive the first equation (N1-N2 in 4:09). Now, this equation makes no mention of the voltage we chose, so it must be true for all choices of voltage. If it was not the case, then there would be no solution If the previous paragraph sounds weird, all I can say is that it may take some time to digest the argument (rereading the second paragraph may help), but, nevertheless, it's a truthful argument. Once you have derived the Delta to Y equations, you have proved nothing (we assumed there was a solution to start with). All you have to do, though, is to check if they really are a solution by direct substituion (for any given three voltages at the nodes, the currents entering the nodes must be the same on the Delta and Y configurations) and the theorem is rigorously proven. No deep circuit theory needed, no superposition; the central argument is purely mathematical, logical. Now, once you've checked the solutions, then to manipulate them to obtain the Y to Delta conversion is legitimate, allowing you to prove rigorously the second theorem. I hope this helps whoever was, like me at the beginning, quite confused by the video and its assumptions.
