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## Health and medicine

### Course: Health and medicine > Unit 2

Lesson 4: Blood pressure- What is blood pressure?
- Learn how a stethoscope can help determine blood pressure
- Resistance in a tube
- Adding up resistance in series and in parallel
- Adding up resistance problem
- Flow and perfusion
- Putting it all together: Pressure, flow, and resistance
- Blood pressure changes over time
- Regulation of blood pressure with baroreceptors

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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.

## Want to join the conversation?

- Are the formulas the same as those used for current flowing through a conductor?(2 votes)
- it's just the same as calculating the total resistance of an electric current with serial/parralel circuit(7 votes)

- There's no units for resistance?(2 votes)
- The universal unit of resistance is Ohm, depicted mathematically by the Greek symbol Omega(3 votes)

- when we have 3 tubes Rt = 10% out of sum of these 3 ?(2 votes)
- I'm not sure if you're asking about the three tubes in parallel or in series.

Let's say all three tubes have a resistance of 2 (R=2).

1) If the tubes are in*series*, then total resistance is the sum of all three resistances.

Rt = R1 + R2 + R3 = 2 + 2 + 2 = 8

2) If the tubes are in*parallel*, then the total resistance is the inverse of the sum of the inverse of all three resistances

Rt = 1 / (1/R1 + 1/R2 + 1/R3) = 1/ (1/2 + 1/2 + 1/2) = 1/(3/2) = 2/3

In either case, Rt is not 10% of the sum of the three resistances. 10% of the sum would be 10% * 8 = 0.8. Keep in mind that I'm only showing you one example that shows that Rt is not always 1-% of the sum of resistance. There may be a situation with the right numbers where total resistance of the three tubes in series could equal 10% of the sum of resistances. However, this is generally not the case, and you should not use this as a hard and fast rule.

In addition, remember that for tubes in series, the total resistance is always greater than the resistances of each individual component (mentioned in the video "Adding up resistance in series and in parallel").(3 votes)

- why is resistance inversely proportional to current?(2 votes)
- is this the easiest way for us to find rt or are there more ways to find rt(2 votes)
- Is current decreases while passing through resistance in series as we know I=Q/t where as t increases continuously as charges lose there energy while passing through resistance(2 votes)
- Isn't it easier to just add up 8+5+5+10+3(1 vote)
- Hi Zoe, I can see why you might think that...but the math you suggest will give you a very different and incorrect result. Try reviewing 'adding fractions with different denominators'. Although you eventually do flip the denominator so that it is in the numerator, it is very important that you do this step last. Here is the Khan video for this: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic/cc-5th-addsub-frac-word-problems/v/adding-fractions-with-unlike-denominators-word-problem(1 vote)

- Two resistors, one of 6 ohms and the other of 3 ohms resistance, are connected in a parallel across a source of emf of 12v

what will be the effective resistance of the combination?(1 vote) - in the beginning why does the smaller one have more resistance?(1 vote)
- For the middle three, they have the same length, but the smaller one's radius is smaller. According to the formula R = (8*L*eta)/pi*r^4, the ones who have the same length and viscosity of the fluid, the smaller the radius is, the bigger the Resistance. So, the smaller one in the middle three has the biggest resistance.(1 vote)

- Thank you for this helpful video but the main vessel is larger and shorter than the upper and lower ones and has a higher resistance and that doesn't even make sense .(1 vote)

## 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.