 In this video, we're going to be looking at determining the neutral current in an unbalanced system. If you go back and watch the video on Y configuration or star configuration determining neutral current in a balanced system, you see that the currents in a neutral always end up being zero amps. We prove that through vector algebra. The same thing holds true when we are discussing current in an unbalanced system. We still have to use that vector algebra and I'll prove it to you. Let's take a look. First things first, let's get our Y system or our delta system set up. So we've got our Y system. I've got three different phases and then I have a neutral, that star point we call it. That's the genius of the Y system. Then we're going to label them. We've got A phase, B phase, C phase and as I said the neutral. Next up, what we do is we get our instantaneous polarities figured out. So again, as the purists will no doubt rail against me, I understand that they're going to be different at different points. I've got negative positive, negative positive, negative positive and it looks like they're all happening at the exact same time. I understand that in a three phase system, each line is going to be 120 degrees at a phase. So they will not be happening at the same time, but the math still works. So let's not get too hung up on that. So let's take a look what we've got here. Let's give some currents to these phases. So I'm just picking these out of the air. I've got 12 amps, I've got 6 amps going through this one, I've got 20 amps going through this one. Again just as with single phase, we know that the neutral carries the unbalanced current. Well these are not balanced. It's not a balanced system. I've got 12 amps here, 6 amps here, 20 amps here, which this is more realistic. You're not going to see very many balanced three phase systems if ever, it's more of a theoretical thing. You will, however, definitely see an unbalanced system. So this is very practical. First thing I do, as you know, I like to get my X, Y chart drawn out there. And again because these are all happening at different times, we have to figure out what their X and their Y coordinates are because we cannot just add 6 to 12 because they're heading in different directions. Then I would tell you to go watch the videos on vector addition if you don't understand what we're talking about at this point. First things first, let's start with B phase because it's all X no Y. So I come in here, I'm going to go negative 6 times the cos of 0 degrees gives me negative 6. Negative 6 times the sine of 0 degrees gives me 0. So that's breaking our 6 amps at 0 degrees into the X and Y coordinate. Then we come in on this phase here and what we're going to do is we're going to go negative 12. You see how I'm entering here and I hit the negative first? Negative 12 times the cos of 120 degrees because we are 120 degrees out of phase gives me 6 amps, or not 6 amps, just gives me 6. And then negative 12 times the sine of 120 degrees gives me negative 10.4. One last but not least, the 20 amps, again it's a negative because I'm hitting that negative first so negative 20 times the cos of 240 degrees gives me 10 and negative 20 times the sine of 240 degrees gives me 17.3. So now what I can do is I can add all these up. I got negative 6 plus 6 is 0 plus 10 equals 10 and 0 plus negative 10.4 gives me negative 10.4 plus 17.3 gives me 6.9. This is my rectangular vector and I've got to figure out, break it into polar form. So I use Pythagoras' theorem, 10 squared plus 6.9 squared equals 12.1 squared. That's a 1 not a 7, 12.1 amps. That's what's going to be on my neutral. With all these different currents coming in here to balance it out the neutral needs to carry 12.1 amps. So in an unbalanced Y circuit you use the vector algebra to calculate your neutral current. Just like we used the vector algebra to prove that in a balanced circuit the neutral current will be 0.