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# Adding up resistance problem

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.