Hey guys. So in this video, I want to go over an example of a network of resistors that looks scarier than it really is. So here we want to find the equivalent resistor of these guys, and it looks really hairy, but I want to show you how you can make it look more familiar to solve this question. Okay. And the key thing we're going to do here is we're going to move the wires around, so that they look more familiar. So for example, the 5 and the 4 are sort of end up at an angle, which is unusual, and it doesn't make it harder to sort of visualize what's really going on here. So the first thing I'm going to do is I'm going to try to make this 4 vertical, and I can actually just move this point here where the 3 of them, 3 wires touch. I can move this point right here, and then imagine if you have a 4 and then you're grabbing the bottom. Right? You're grabbing the bottom and just doing this. K? So if I do that, let's redraw. I'm going to get a 2 at the top, a 3 here, and then this red point right here is now going to be right here. So that I get a 4 like this and then there's still a 5 here. Let's leave that alone. We'll take this slowly. And now this hopefully looks, more familiar. The other thing we can do is notice that this is a single branch right here. That's all along this green line. There are no points where the wire splits. Now obviously, the wire splits here and the green dot splits in the red dot, but within those two dots, nothing splits. What that means is that you can actually move the 3 and just redraw the 3 over here and it's exactly the same thing. It functions just the same. So now we get something a little cleaner. And I'm going to draw again. I'm going really slowly, because I want to make sure you fully understand this. K? And now it looks like this. And hopefully, now this looks super familiar. Hopefully, you'd see that this is a branch with a single resistor in it. And this is a branch here also with a single resistor on it or in it. And because you have 2 resistors on opposite sides, they're alone on opposite sides of this loop here, they are in parallel. So these 2 guys are in parallel so I can combine them. K? Usually, I would keep going, but just just for the sake, of just getting this over with, let's just combine these 2 real quick. And because I have 2 resistors in parallel, I can use the shortcut equation. The equivalent resistance is going to be remember the pyramid, it's of times on top and plus on the bottom. Okay? So it's going to be 4×34+3 which is 12/7, which is approximatley 1.7 ohms. K? So this entire thing can be redrawn as all of this. Right? Can be redrawn. There's a 2, there's a 5, and instead of having a 4 and then a 3, I'm just going to have a single 1.7 right here. And now, this is a little simpler because I have 3 on top a little bit and then I'm going to move the bottom a little bit. And then I'm going to move the bottom a little bit. So I'm going to move the top a little bit and then I'm going to move the bottom a little bit. So really slowly here, the 5 is going to be moved over here and this part of the 5 is going to be moved over here so that it forms sort of a straight line. And this is going to look like this. Got a 2 and then you got a 5 straight down and then there's still the 1.7 over here. Now the 1.7 is kind of like this. Right? If you curve the 1.7, it's kind of straight like this. I can extend this wire and make it look like this. K? All these are equivalent. You just have to be careful to redraw them correctly. Otherwise, you made up a new circuit, and obviously, it's going to be wrong. K? Again here, hopefully, you see that you have a branch with a single resistor. And then here, you have a branch with a single resistor. And because you have 2 resistors that are alone on their branches, on their opposite sides, they are also in parallel. And once again, I can use the parallel shortcut equation because I have 2 resistors. The equivalent resistance is going to be 5×1.75+1.7 K? And if you do this in a calculator, you get approximately 1.31 ohms. I want to quickly remind you of something that we talked about, earlier, which is whenever you combine things in parallel, the total resistance is smaller or lower than all of the resistances. So it's going to be lower than the 5 and it's going to be lower than the 1.7. Notice that when I merge them, I got a 1.3 lower than 1.7. It makes sense. You can use that to validate that you're probably correct. So finally here, I can draw the 2 and then this entire thing here gets replaced instead of there being 2 of them, there's going to be just a single one point three and these are the points that we have there. Now notice that EIF
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Combining Resistors in Series & Parallel
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