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Current time:0:00Total duration:10:33

Adding up resistance in series and in parallel

Video transcript

you talked a little bit about the resistance equation that we got from dr. plus oo and the equation looked a little bit like this so we had actually let me just replace this we had eight times ADA which was the viscosity of blood times the length of a vessel divided by pi times the radius of that vessel to the fourth power and all of this put together gives us the resistance in a vessel so thinking about just a little bit more let's let's assume for the moment that the blood viscosity is not going to change certainly won't change from moment to moment but let's say that in general blood viscosity is pretty constant now given that if I want to change the resistance that I have two variables left right I've got the length of my vessel and I've got the radius so if I have a vessel like this and let's say it's got a certain radius and length and let's say that radius is R and the length is here and I apply number let's say the number is two for the resistance well I have two options for changing that resistance if I want to increase the resistance I can do two things so let's say I want to increase that resistance and you can look at the equation tell me what that answer would be two things and I'll actually draw it out so one thing would be to keep the radius basically the same but make it much longer right because if I make it longer then since the L is now let's say twice as long and the R is the same now my resistance is going to double so now we go to x + 2 times 2 is 4 so my resistance is 4 okay option 2 let's say I don't want to change the length so I keep the length the same and instead I could actually maybe change the radius and let's say 1/2 the radius and make it half of what it was and actually worked out the mass and the last one and it turned out that if you have the radius in the last video that is then the resistance actually is 16 times higher and you can see that because the resistance equals R to the fourth power here R is to the fourth power so because R is to the fourth power when you have it it goes up sixteen fold and so 16 times 2 is 32 so my resistance is 32 so these are the two strategies if you think of it that way that blood vessel can use to increase resistance and of the two you can see that one of them is definitely more effective I mean I can see that because it's raised to the fourth power this is going to work much more effectively to raise resistance then changing the length in additional if you think about kind of from a practical standpoint keep in mind that I have smooth muscles so it's actually pretty easy to accomplish this or at least possible to accomplish this whereas trying to actually change the length which is option 1 is not feasible right I mean it's much much more complicated to actually expect a vessel to simply double in its length because it wants to raise resistance so for multiple reasons changing radius again becomes the the name of the game okay so let's complicate this a little bit let's say instead of one vessel I've got three vessels I've got let's say one vessel here and there's this is let's say five and I've got let's say a longer vessel here and this one happens to have a resistance of let's say eight because it's longer and let's do same radius for all these but shorter now this one is two and I want blood to flow through all three of these what is my total resistance and here we're talking about the three vessels being in a series meaning that you actually expect the blood to go through all three of the vessels or tubes so if they're going to go through all three tubes what you have to do is simply add up the total so resistance total so this is total resistance and I just put a little T to remind me that that means total so total resistance equals the resistance of one part plus the second part plus the third part and if you had a fourth or fifth part you just keep adding them up so in this case you have five eight and two so RT becomes five plus eight plus 2 and that equals 15 so total resistance would be 15 and actually I'm going to give you a general rule so total resistance is always always greater then any component and you can see how this is very intuitive right I mean how could how could you possibly have a situation where if you're just simply adding them up you know because we don't expect any negative resistance you know in this situation you're simply adding up all these positive resistances of course the total will be always greater than any one component right seems intuitive but I just wanted to spell it out so now let's take a scenario where you have a human body a vessel in the body and let's say you have three parts to it and these are equal parts so let's say the resistance here is two two and two and you have obviously I want to calculate as before my total so my total will be 2 plus 2 plus 2 which is 6 and then an interesting thing happens so you have let's say I'll draw the same vessel again really interesting thing happens this is the same blood vessel but now you have a blood clot and this blood clot is floating through the blood vessels and it kind of makes its way to this one this one that we're working with and it goes and lodges right here so right here you have a large blood vessel Wow that's pretty big but it's right enough middle third of our of our vessel so we have now a tiny little radius here right it's about let's say half of what we had before so this is the new radius equals half of what the old radius was and you know from the from the last example that's going to increase the resistance in that part by 16 so the the resistance here stays it to here stays it to but here in the middle it goes from 2 to 32 because it's 16 times greener so you end up increasing the resistance in the middle section by a lot so let me just write that out for you the 2 times 16 gets us to 32 so here the resistance is 32 and so if I want to calculate the total resistance I'd get something like this 32 plus 2 plus 2 is 36 so I actually went from 6 to 36 when this blood clot came and clogged up part of that vessel so just keep that in mind we'll talk about that a little bit more but I just want to use this example and also kind of cement the idea of what you do with resistance in a series now let's contrast that to a different situation and this is when you have resistance in parallel so instead of asking blood to either kind of go through all of my vessels I could also do something like this I can say well let's say I have three vessels again and this time I'm going to change the length and the radius and I'd say I have this one's really big let's say and the the resistance here let's say is five here's 10 and here is 6 right we've got three different resistances and the blood now can choose to go through any one of these paths it doesn't have to go through all three so how do I figure out now what the total resistance is so what is the total resistance well the total resistance this time is going to be 1 over 1 R 1 one over r2 plus one over r3 and you can go on and on this is before but in this case we only have three so let's just put that there that there and that there and I can figure this out pretty easily so I can say 1 over 1 over 6 plus 1 over 1 over 10 plus up it and the common denominator there is 30 so I could say 5 thirtieths this is 3 thirtieths and it would be 6 thirtieths and adding that up together I get 1 over 14 thirtieths or 30 over 14 which is 2 and let's say point 1 the to point 1 so the total resistance here is 2 point 1 putting all three of these together pretty interesting and I want you to realize that the resistance in total is actually less than any component part so unlike before where we said that the total resistance is greater than any component here an interesting feature is that you have total resistance is always less than any component so pretty cool set of rules that we can kind of go forward with