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# Adding up resistance in series and in parallel

Learn about how resistance can be added up in series and in parallel (similar to electrical circuits!). Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.

## Want to join the conversation?

• How can you check your own blood pressure?
• You can't manually check your blood pressure without proper equipment, i would recommend getting a blood pressure cuff, which is placed on the upper arm, and it accurately measures your blood pressure.
• At the beginning of the video you said that 'RT" is always greater then any component, then why did you say that it is less then any component at the end of the video.
• Because these are different circumstances.

Rishi first explains circumstance 1, Series of blood vessels: Blood goes through n number (n > 1) consecutive blood vessel. Then the Total resistance would be greater than any resistance in a component because you're adding up all the resistances in the components and as Rishi said, their is no negative variable in the formula calculating resistance.

Rishi first explains circumstance 2, Parallel blood vessels: Blood has an option of going into n (n > 1) different blood vessels. Then the total resistance would be less than any single component because the formula for the total resistance in this case is:

(Let R be resistance)

1 / 1/R1 + 1/R2 + 1/R3 ...

Therefore, the total resistance in this case will be less than any of the components' resistance.

I hope I answered your question, tell me if you want it in simpler words. :D
• why in case of parallel we not simply sum all the values like in series one ?
• Because that's not how physics works but let me give an analogy: forcing a water to go through a tube that is first narrow then wide then narrow again, has a higher resistance than splitting the tube into 2 narrow and 1 wide tube because the current can split and flow through different resistors.
• I may just not have picked it up over the last few videos, but what is/are the unit(s) for the resistance here?
• if you know the Poiseuille's law for resistance (what is used here) and what each symbol represents, you can see what are the possible units for each "symbol": for example you can do it in SI

R = (8nL)/ (πr^4)

L = length of pipe = m
r = pipe radius = r
n = fluid viscosity = Poise

Note: a “Poise” because we are talking about Dynamic viscosity (the measurement of the fluid's internal resistance to flow)

there can be other versions based on what standard you use
• , if we cut the system of vessels before the vessel with R=5, the resistance in the other 2 will drop to 0 because there would be no flow in them, am i right? so the Rt equals R=5.. So its not always greater it can be same as well... correct me if im wrong, i just wanted to discover a situation that doesnt match theory :p
• From Poiseuille's law, R = (8μLQ) / (πr⁴). The most important variable in this scenario is Q, which is flow through the vessel. If we imagine that a clamp has been put on the vessel before those segments, then flow is completely stopped. Because Q = 0 in this scenario, R must therefore also be 0 to satisfy the equation.
• In reality wouldn't the viscosity in the veins increase as some of the less viscus plasma has left for the lymph system? This would leave behind a greater proportion of heavier proteins in the venous part of circulation. If this is true, would you factor this into the equation in 'real life'? ...but then the volume passing would also decrease. I'm running in circles in this. Can someone please help? (I understand the math in the video so no need to go over that again). I think I'm mostly having trouble with why blood pressure drops in the venous system after blood has left the capillaries. ...all the tubes in parallel join up again, after all...
• I think blood pressure drops in the venous system because the veins are more distensible (i.e. can accommodate more volume of blood) than the arteries. Therefore, between an artery and a vein (both holding the same volume of blood), the former has a higher pressure.

In the capillaries, not all plasma in the blood goes into the interstitial fluid. There must be equilibrium between the two compartments. What actually happens in the capillaries is that oxygen and nutrients go out to the interstitial fluid and at the same time, wastes are being collected from the interstitial fluid.

I hope I answered your question. Feel free to correct me if I'm wrong! Cheers :)
• when we found the resistance in the seria, where the tubes connected to each other or separeted? . when we found the resistance in the parallel and suppose I measure resistance in one of the tubes will I not get a difference resistance because they have difference raduis? So what is the resistance that we found in the parallel telling us?
• First question: When we found the resistance in the series, where the tubes connected to each other or separated?

Connected, or else you are bleeding for life or have a constantly growing bruise.

Second question: When we found the resistance in the parallel and suppose I measure resistance in one of the tubes, will I not get a difference resistance because they have different radii?

Yes, Rishi explained that in the video, that's why there are tubes with resistance 5, 6, and 10.

Third question: So what is the resistance that we found in the parallel telling us?

Let's suppose the 3 branching blood vessels are arterioles branching off of a small artery and the arterioles have the resistance of 5, 6, and 10. We would be finding the resistance of the total resistance of the blood inside these 3 vessels.

• It seems like blood pressure resistances have the same formula as electrical circuit resistances. Am i correct ?
• no. the blood pressure resistance uses the Hagen–Poiseuille equation while electricity uses Ohm’s law. The equations are different. They have the same idea but use different variables so describe it in different ways based on what information is known.

difference between fluid flow and electric current (why the same formula cannot be used): Electron velocity does not depend on the distance to the walls of the conductor. The resistance is due to the interaction between the flowing electrons and the atoms of the conductor"

source:
https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation