0:00:00.000,0:00:01.650


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We had talked a little bit[br]about the resistance equation

0:00:04.150,0:00:06.020
that we got from Dr. Poiseuille.

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And the equation looked[br]a little bit like this.

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Actually, let me[br]just replace this.

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We had 8 times eta, which[br]was the viscosity of blood

0:00:17.860,0:00:20.650
times the length[br]of a vessel divided

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by pi times the radius of that[br]vessel to the fourth power.

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And all this put together gives[br]us the resistance in a vessel.

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So thinking about this[br]a little bit more,

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let's assume for the moment[br]that the blood viscosity is not

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going to change.

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It certainly won't change[br]from moment to moment,

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but let's say that, in[br]general, blood viscosity

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is pretty constant.

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Now, given that, if I want[br]to change the resistance,

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then I have two variables left.

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I've got the length of my[br]vessel and I've got the radius.

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So if I have a vessel--[br]like this-- and let's

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say it's got a certain[br]radius and length.

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And let's say that radius is[br]r, and the length is here.

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And I apply a number.

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Let's say the number is[br]2 for the resistance.

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Well, I have two options for[br]changing that resistance.

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If I want to increase[br]the resistance,

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I can do two things.

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So let's say I want to[br]increase that resistance.

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And you can look at the[br]equation and tell me

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what the answer would be.

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Two things.

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And I'll actually draw it out.

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So one thing would be to keep[br]the radius basically the same,

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but make it much longer.

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Because if I make it[br]longer, since the L is now,

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let's say, twice as[br]long and r is the same,

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now my resistance[br]is going to double.

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So now we go 2 times.

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And 2 times 2 is 4.

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So my resistance is 4.

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OK.

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Option 2.

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Let's say I don't want[br]to change the length.

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I keep the length the same.

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Instead, I could actually[br]maybe change the radius.

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And let's say I half the radius.

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I make it half of what it was.

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And I actually worked out[br]the math in the last one.

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And it turned out that,[br]if you half the radius--

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in the last video, that is--[br]then the resistance actually

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is 16 times higher.

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And you can see that because[br]the resistance equals

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r to the fourth power here.

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So because r is to the fourth[br]power when you half it,

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it goes 16-fold.

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And so 16 times 2 is 32.

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So our resistance is 32.

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So these are the two strategies,[br]if you think of it that way,

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that a blood vessel can[br]use to increase resistance.

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And of the two, you can[br]see that one of them

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is definitely more effective.

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I mean, I can see[br]that because it's

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raised to the fourth[br]power, this is

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going to work much more[br]effectively to raise

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the resistance than[br]changing the length.

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And additionally,[br]if you think of it

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kind of from a[br]practical standpoint,

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keep in mind that I[br]have smooth muscle.

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So it's actually pretty[br]easy to accomplish this--

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or at least possible[br]to accomplish this.

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Whereas trying to[br]actually change

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the length-- which is[br]option 1-- is not feasible.

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I mean, it's much, much more[br]complicated to actually expect

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a vessel to simply[br]double in its length

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because it wants to[br]raise the resistance.

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So for multiple reasons,[br]changing radius,

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again, becomes the[br]name of the game.

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OK.

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So let's complicate[br]this a little bit.

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Let's say instead of one[br]vessel, I've got three vessels.

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I've got, let's say,[br]one vessel here.

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And there's, let's say, 5.

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And then I've got, let's[br]see, a longer vessel here.

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And this one happens to have[br]a resistance of, let's say, 8

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because it's longer.

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And let's do the same radius[br]for all these, but shorter now.

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This one is 2.

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And I want blood to flow[br]through all three of these.

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What is my total resistance?

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And here we're talking[br]about the three vessels

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being in a series--[br]meaning that you actually

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expect the blood to[br]go through all three

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of the vessels or tubes.

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So if they're going to go[br]through all three tubes, what

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you have to do is[br]simply add up the total.

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So resistance total-- so[br]this is total resistance.

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And I just put a[br]little t to remind me

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that that means total.

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So total resistance equals[br]the resistance of one part

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plus the second part[br]plus the third part.

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And if you had a[br]fourth or fifth part,

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you just keep adding them up.

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So in this case, you[br]have 5, 8, and 2.

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So Rt becomes 5 plus 8[br]plus 2, and that equals 15.

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So total resistance would be 15.

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And actually, I'm going to[br]give you a general rule.

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Total resistance is[br]always, always greater

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than any component.

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And you can see how[br]this is very intuitive.

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I mean, how could you possibly[br]have a situation where--

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if you're just simply[br]adding them up,

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because we don't expect[br]any negative resistance

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in this situation.

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You're simply adding up all[br]these positive resistances.

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Of course, the total[br]will be always greater

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than any one component.

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Seems intuitive, but I just[br]wanted to spell that out.

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So now, let's take[br]a scenario where

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you have a human body,[br]a vessel in the body.

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And let's say you have[br]three parts to it,

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and these are equal parts.

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So let's say the resistance[br]here is 2, 2, and 2.

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Obviously, I want to calculate--[br]as before-- my total.

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So my total will be 2[br]plus 2 plus 2, which is 6.

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And then, an interesting[br]thing happens.

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So you have, let's say-- I'll[br]draw the same vessel again.

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A really interesting[br]thing happens.

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This is the same blood vessel,[br]but now you have a blood clot.

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And this blood clot is floating[br]through the blood vessels.

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And it kind of makes[br]its way to this one

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that we're working with.

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And it goes and[br]lodges right here.

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So right here you have[br]a lodged blood vessel.

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Wow.

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That's pretty big, but it's[br]right in that middle third

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of our vessel.

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So we have now a tiny[br]little radius here.

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It's about, let's say,[br]half of what we had before.

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The new radius equals half[br]of what the old radius was.

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And you know from[br]the last example

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that's going to increase the[br]resistance in that part by 16.

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So the resistance[br]here stays at 2.

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Here it stays at 2.

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But here in the middle,[br]it goes from 2 to 32

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because it's 16 times greater.

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So you end up increasing[br]the resistance

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in the middle section by a lot.

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So let me just write[br]that out for you.

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So 2 times 16 gets us to 32.

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So here the resistance is 32.

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And so if I wanted to[br]calculate the total resistance,

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I'd get something like this--[br]32 plus 2 plus 2 is 36.

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So I actually went from 6[br]to 36 when this blood clot

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came and clogged up[br]part of that vessel.

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So just keep that in mind.

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We'll talk about that[br]a little bit more,

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but I just wanted[br]to use this example

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and also kind of[br]cement the idea of what

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you do with resistance[br]in a series.

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Let's contrast that to[br]a different situation.

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And this is when you have[br]resistance in parallel.

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So instead of asking[br]blood to either kind of go

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through all of my vessels,[br]I could also do something

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like this-- I could[br]say, well, let's say,

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I have three vessels again.

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And this time, I'm[br]going to change

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the length and the radius.

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And let's say this[br]one's really big.

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And the resistance here,[br]let's say, is 5, here is 10,

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and here is 6.

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So you've got three[br]different resistances.

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And the blood now[br]can choose to go

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through any one of these paths.

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It doesn't have to[br]go through all three.

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So how do I figure out now[br]what the total resistance is?

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So what is the total resistance?

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Well, the total[br]resistance this time

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is going to be 1 over 1 R1,[br]plus 1 over R2, plus 1 over R3.

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And you can go on and[br]on just as before.

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But in this case,[br]we only have three.

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So let's just put that there,[br]that there, and that there.

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And I can figure this[br]out pretty easily.

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So I can say 1 over 1 over[br]6 plus 1 over 10 plus 1/5.

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And the common[br]denominator there is 30.

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So I could say 5/30.

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This is 3/30, and[br]this would be 6/30.

0:09:32.900,0:09:42.130
And adding that up together,[br]I get 1 over 14/30 or 30

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over 14, which is 2[br]and let's say 0.1.

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So 2.1.

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So the total[br]resistance here is 2.1.

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Putting all three of these[br]together is pretty interesting.

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And I want you to realize[br]that the resistance in total

0:10:00.990,0:10:03.020
is actually less than[br]any component part.

0:10:03.020,0:10:07.640
So unlike before where we said[br]that the total resistance is

0:10:07.640,0:10:12.610
greater than any component,[br]here an interesting feature

0:10:12.610,0:10:17.950
is that you have[br]total resistance

0:10:17.950,0:10:27.100
is always less[br]than any component.

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So a pretty cool set of rules[br]that we can kind of go forward

0:10:30.630,0:10:31.941
with.

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