 In this video we're going to talk about three phase theory and the Y configuration and we're going to be talking specifically about voltages. And we're going to narrow in on the phase voltage and the line voltage in a Y configuration. What we have here is a basic Y config. We've got a reason why it's called a Y configuration and that's going to blow your mind is it looks like a Y. There you go. And one thing that we don't have in this figure and we'll discuss in later videos is there's a neutral point. We have this sometimes it's called a star point because we have this star here kind of stars off and we can neutral from there and we can end up using two different voltages when we're dealing with a Y configuration. But right now let's talk about how we can figure out what our phase voltage is which is would be this just across this winding or just across this winding or just across this winding or the line voltage which would be this voltage to this voltage. It's going to be a little bit different. So I have three different lines here. I have line A, line B, line C, red, black, blue or however you want to look at it. And if I see I've got a phase voltage here if I want to figure out what my A voltage A to V, B, sorry, voltages it's going to be from A across this winding plus this winding. However, we cannot add these arithmetically meaning if this is 120 volts and this is 120 volts I can't add 120 plus 120 because you might notice that there's a bit of an angle here. In fact, there is a 120 degree angle here so we can't add them arithmetically. We have to add them in what's called vectorally. And if you want to know more about how to add vectors you can go back into the videos on how to add vectors. I'm going to assume that you have some knowledge of it in this video so we'll move on from here. Alright, I have assigned the phase voltage. So when we're determining a voltage across the windings in a Y config the phase voltage is what it is. It's 120 volts, 120 volts, 120 volts. The next step that I use when I teach how to add these voltages to get the line voltage is I just pick what's called instantaneous polarity. I'm going to say that this point is negative and that point is positive. This point is negative and this point is positive. This point is negative and this point is positive. Now I know it's an oversimplification because they are rotating around I know for all you physics majors out there you'll be talking about how this point and this point aren't negative at the exact same time. That's okay I understand that but right now just for simplicity's sake we're going to assume that these points are negative at the same time when we go ahead and add them. Now I've got to work out my angles. The way that I've got this drawn out is I've got 90 degrees up top here and then 120 degrees later I have 210 degrees and 120 degrees later I have 330 degrees. So what we're going to do is I'm going to show you how we're going to add A plus to B here and it looks really complicated because I've got all these positives and negatives and numbers and angles but it's really not that difficult. The first thing I do when I add vectors is I come up with an XY chart because every angle can be broken down into an X component and a Y component. So we're going to look first at phase A here and we're going to see that it is all on a Y axis and nothing on an X axis. So you could say that your X is zero and our Y at this point is going to be positive 120 because what we're doing here is I'm adding from this point so I'm going to be a positive to negative so I'm saying it's positive 120. If I was moving back the other way I would say it is negative 120 but I'm not I'm moving from this point to this point which will be positive 120. So filling in my XY chart there I've got zero on my X positive 120 on my Y. Now coming around the corner here I've got a negative 120 but it is at 330 degrees. So what we have to do is, again go back to the videos on how to add vectors, is I'm going to take the cosine of 330 degrees and multiply it by negative 120. And then I'm going to take the sine of 330 degrees and multiply it by negative 120. The cosine will give me the X, the sine will give me the Y. Plug that in three calculators and you get negative 104 on my X and positive 60 on my Y. So I've got my X coordinates and my Y coordinates for A phase. I've got my X coordinates and Y coordinates for B phase. And now all I have to do because these guys are heading in the same direction somewhat the X's can add together and the Y's can add together. And I get negative 104 on my X and positive 180 on my Y. That is known as rectangular and from there we can figure out what our resultant is, which would be our overall voltage. So what I'm gonna do is use Pythagoras and just go negative 104 squared plus 180 squared gets me the square root of, again go back to the videos on how to add vectors and I get 208 volts. So from this point to this point adding them up vectorially and not arithmetically I end up with 208 volts. You can do that with any point if you added A to C here. You do the same thing except I'd be going negative 120 times the cos of 210. Negative 120 times the sine of 210 would get me my X and my Y. Now if we take 208 and divide it by 120, we get 1.732 which is the square root of three or root three. So you'll often hear it said that when you're dealing with Y in a voltage, you take the phase voltage and multiply it by root three. So we just proved mathematically why that is so. So you can say that in a Y voltage configuration, the E line is equal to E phase times root three or 1.732.