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Adding up resistance problem

Here's a chance to see if you can combine what you know to add up resistance in series AND in parallel. Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.

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Video transcript

Let's say you've got a blood vessel here, and it's a longish blood vessel, and we'll give it a resistance of 8, and it has three branches. Say two big ones and kind of a tiny one in the middle, and this goes straight across. And this has a resistance of 10, and these biggish ones, they have resistance of, let's say, half that. So they're about 5. And on this side they all come together again and enter a short vessel, and this has a resistance of 3. So my question to you is what is the total resistance of blood going in here and out here? So it's going to have to go through this 8 bit, and then it has three choices here, here, here, or here. But eventually they all come together again into that 3 bit and then exit out the other side. So what is the total resistance? So what is RT for this? That's the question. And what I'm going to do is I'm going to divide into two parts. Part one, I'm going to figure out in part one what the resistance is for this part right in here. So I can do that using an equation I introduced in the last video, which was you can basically take RT, which is total resistance for that yellow box, equals 1 over 1/5 plus 1/10 plus 1/5. And I can look at that and tell you the common denominator is going to be 10, right, for all three. And here the numerator, I've got 2, 1, and 2. So putting it all together I've got 1 over-- what is that-- 5/10, and that equals 10/5, which equals 2. So that tells me that the resistance in this middle yellow box is 2. And that makes sense with our rule, because we said that when things are in parallel, the total resistance is going to be less than any component. And, in fact, 2 is less than 5, 10, and 5, right? It's less than any of those numbers individually. So we've got now in part two, we have three things in series, right? We basically have something like this. We have 8 and we have 2 and we have 3. So we've got basically three things in a series, and so we simply add those up. So I'm going to say RT now equals 8 plus 2 plus 3. And so RT equals 13. So if I want to know what is my total RT, my total resistance, I would say it is 13. So that's the answer to this problem, and what I want to get you thinking about is total resistance for the body, the human body, which has obviously more than just a few vessels like I have in this diagram. We have literally thousands and thousands of vessels.