Weird Arrangement (Re-Drawing Resistors)

by Patrick Ford
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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 Harry, but I want to show you how you can make it look more familiar to solve this question. Okay. And that you think we're gonna do here, is we're gonna move the wires around, um, so that they look more familiar. So, for example, um, the five and the four are sort of at an angle, which is unusual. And it doesn't. It makes it harder to sort of visualize what's really going on here. So the first thing I'm gonna do is I'm gonna try to make this four vertical, and I can actually just move this point here where the three of them three wires touch. I can move this point right here and then imagine if you have a four and then you're grabbing the bottom right? You're grabbing the bottom and just doing this, Okay? So if I do that, let's redraw. I'm gonna get a two at the top. That's three here and then this red point right here is now going to be rights here so that I get a four like this. And then there's still a five here. Let's leave that alone. Will take this slowly. And now this hopefully looks, um, mawr familiar. The other thing we could 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 in 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 three and just redraw the three over here. And it is exactly the same thing. Functions just the same. So now we get something a little cleaner, and I'm gonna draw again. I'm going really slowly because I wanna make sure you fully understand this. Okay? And now it looks like this, and hopefully now this looks super familiar. Hopefully you'll 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 two resistors on opposite sides there, alone on opposite sides of this loop. Here they are in parallel. So these two guys are in parallel so I can combine them. Okay, Usually I would keep going, but just just for the sake of just getting this over with, let's just combine these two real quick. And because I have two resistors in parallel, I can use the shortcut equation. The equipment resistance is going to be Remember the pyramid? It's times on top and plus on the bottom. Okay, so it's gonna be four times three, divided by four plus three. This is 12 divided by seven, which is one 17 So this entire thing can be redrawn as a. This whole thing here actually can think of it as all of this can be redrawn. There's a two, there's a five, and instead of having a four and then the three, I'm just gonna have a single 1.7 right here and now this is a little simpler because I have three instead of two. Now, what about this other five here? I fixed the four, made it straight. Let's make the five straight and the five like this. So I'm gonna move the top a little bit, and then I'm gonna move the bottom a little bit so really slowly here, the five is gonna be moved over here, and this part of the five is gonna be moved over here so that it forms sort of a straight line, and this is going to look like this. Got a true and then you got a five straight down, and then there's still the the seven over here. Now the seven sort of like this, right? If you curve the the seven is kind of like, straight like this, the 1.7 rather. But I could extend this wire and make it look like this. Okay. All these air equivalent, you just have to be careful to redraw them correctly. Otherwise, you made up a new circuit, and obviously it's gonna be wrong. Okay. 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 two resistors that 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 two resistors. The equipment resistance is going to be five times 1.7, divided by five plus 1.7. And if you do this in the calculator, you get 1. 1.3. 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 the all of the resistance is. So it's gonna be lower than the five. And it's gonna be lower than the 1.7 notice that when I emerged 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 two, and in this entire thing here gets replaced. Instead of there being two of them, there's gonna be just a single 1.3. And these are the points, um, that we have there now notice that between these two guys there's a direct connection between them. There's no forks between them, which means that they are in Siris and finally, serious resistors are just added um s 02 plus 1.3 is 3.3. So the equivalent resistance of that big old mess is just 3.3 OEMs. So please do know that you can take the liberty to move some wires around to make things look more familiar to you. Different people see things a little bit differently, and they prefer their resistance to be organized differently in the book Might throw you book. A professor might throw you some some questions that are drawn in a weird way to see if you really know what's going on. Take some liberty to draw them, but please make sure they do it correctly. Cope. That's it for this one. Let's get going.