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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.

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  • blobby green style avatar for user Charles Z
    Are the formulas the same as those used for current flowing through a conductor?
    (2 votes)
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  • leaf orange style avatar for user akthomas19
    There's no units for resistance?
    (2 votes)
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  • leaf green style avatar for user Mihai Marian
    when we have 3 tubes Rt = 10% out of sum of these 3 ?
    (2 votes)
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    • piceratops ultimate style avatar for user Sofia Hu
      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)
  • starky tree style avatar for user Shubhom Tenginkai
    why is resistance inversely proportional to current?
    (2 votes)
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  • duskpin sapling style avatar for user Kathryn
    is this the easiest way for us to find rt or are there more ways to find rt
    (2 votes)
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  • blobby green style avatar for user Aimen Arshad
    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)
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  • starky sapling style avatar for user Storm
    Isn't it easier to just add up 8+5+5+10+3
    (1 vote)
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  • blobby green style avatar for user It'sOfficiailly YoungRed Muf Fin
    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)
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  • leaf red style avatar for user Sam Daliya
    in the beginning why does the smaller one have more resistance?
    (1 vote)
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    • boggle purple style avatar for user lily J
      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)
  • aqualine ultimate style avatar for user Mina Ragy
    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)
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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.