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Finding the Effective resistance of a tree of resistors

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  1. Sep 30, 2014 #1
    1. A) Find the Effective resistance of a tree of resistors that bifurcates 3 times.
    B) Find the effective resistance of a tree of infinite resistors. (if the tree below went on to infinity)

    EMWxPz6.jpg

    2. Relevant equations
    Ohm's Law

    3. The attempt at a solution
    I have no idea how to start this. There was no other info given either.
     
    Last edited by a moderator: Apr 17, 2017
  2. jcsd
  3. Sep 30, 2014 #2

    phinds

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    Surely you can draw the 3-bifurcation one to completion and solve it? At least give it a try.
     
  4. Sep 30, 2014 #3
    is it just resistors in series ?
     
  5. Sep 30, 2014 #4

    NascentOxygen

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    Let's denote the resistance of that whole tree as T ohms. We don't know what it will be, yet, but at least we have given it a symbol.

    Wherever you look, you find sub-trees that are all identical to that parent. So in place of each of those sub-trees going off to infinity you can substitute a single resistor of value T ohms. This simplifies the figure considerably!! !!
     
  6. Sep 30, 2014 #5
    So theres 7 T ohms + R ohms
    im just having a hard time seeing if they are in series or parallel
     
  7. Sep 30, 2014 #6

    NascentOxygen

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    I think you mean 8? These will all be going to ground at their farther end.

    See whether you can do it using fewer than 8.
     
  8. Sep 30, 2014 #7
    is the answer 15R/8 ohms?
     
  9. Sep 30, 2014 #8
    and for part b would it just be 1 since theres a infinite number of resistors and bifurcations?
     
  10. Oct 1, 2014 #9

    NascentOxygen

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    For (a), yes.
     
  11. Oct 1, 2014 #10

    NascentOxygen

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    You're guessing.

    The resistance is going to have to be at least R.
     
  12. Oct 1, 2014 #11

    phinds

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    Good job !
     
  13. Oct 1, 2014 #12
    so the answer to part b is R ohms because it would be infinity over infinity?
     
  14. Oct 1, 2014 #13

    phinds

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    If you want to really get a sense of what's going on, do it for 1 branch, 2 branches, 3 branches (already done), and maybe 4 branches and see if there is a pattern that you could extrapolate to a limit.
     
  15. Oct 1, 2014 #14
    oh ok. so its 2R ohms since is approaching 2R ohms. The next branch added would be 31R/16
     
  16. Oct 1, 2014 #15

    phinds

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    Again, good job !
     
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