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How to calculate the equivalent resistance using wye delta ?

  1. Jan 2, 2016 #1
    1. The problem statement, all variables and given/known data
    https://z-1-scontent-sin1-1.xx.fbcdn.net/hphotos-xtf1/v/t34.0-12/12435980_942112312550457_1708451532_n.jpg?oh=b29a5e9b2ff96bbf0e11932d081eb25e&oe=568A9B79


    We need to find the equivalent resistance along A to B ie AB
    2. Relevant equations
    R=(1/R1 + 1/R2+.........+1/Rn)^-1 , Y-Delta transformation , equation for parallel combination, equation for series combination.
    3. The attempt at a solution
    I tried wye-delta but my teacher says that I need not use wye-delta .How possible? I have two answer 1.43 ohms and 1.6 ohms .What is the actual equivalent resistance? Can you please solve these problems?
     
    Last edited: Jan 3, 2016
  2. jcsd
  3. Jan 3, 2016 #2
    Is there any other way?
     
  4. Jan 3, 2016 #3

    cnh1995

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    Well, I believe wye-delta will give you the answer since there are a lot of wyes and deltas in the circuit, but I think there is other way(simpler, maybe). Consider the two 2Ω resistors in the middle, which are parallel to AB. Replace each of them by a parallel combination of two 4Ω resistors. Now cut the circuit into two halves along the horizontal symmetry, separating the 4Ω resistors.
     
  5. Jan 3, 2016 #4
    Then what will be the equivalent resistance?
     
  6. Jan 3, 2016 #5

    cnh1995

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    Lets call the side along which we cut the circuit as CD Now, the equivalent resistance( between A and B )of the lower part and equivalent resistance of the upper part(between C and D) will be in parallel, which will give you net resistance between A and B. Out of that, equivalent resistance of the lower part is very easy to find, just by series-parallel combination. But for the upper part, I think you need to use wye-delta at least once(or twice). Seems that you can't get rid of wye-delta so easily! But I think the no of wye-delta conversions is reduced this way.
     
  7. Jan 3, 2016 #6

    cnh1995

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    In the upper part, you only need to use wye-delta once. Then the upper part becomes a balanced Wheatstone's bridge and RCDwill be easy to calculate.
     
  8. Jan 3, 2016 #7
    Can you calculate the equivalent resistance please .I am getting 1.43 ohms and 1.6 ohms as the answer in different cases. Can you tell me the answer, please :3
     
  9. Jan 3, 2016 #8

    cnh1995

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    Well I'm afraid telling the final answer is not allowed here and if I did so, it will be removed immediately and I'll be warned:wink:! It will be helpful if you drew and posted the diagrams here. What answer have they provided? I just want to verify if my approach is right. Otherwise, it will waste your precious time.
     
  10. Jan 3, 2016 #9

    cnh1995

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    Nope, this approach is not right. We are calculating the resistance between A and B. So, lower part resistance will be between A and B but upper resistance will be between C and D. They are not in parallel. I ran a quick simulation on my phone and verified it. That was a silly mistake! But I think there should be some other method since the configuration is symmetric. I'll try to work it out!
     
  11. Jan 3, 2016 #10

    epenguin

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    Last edited: Jan 3, 2016
  12. Jan 3, 2016 #11

    cnh1995

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    Well, the shortest way I got is delta-wye conversion itself. One on upper side and one on the lower side(viewed from AB).
     
  13. Jan 3, 2016 #12
    The shortest way is circuit symmetry which provides Equivalent Resistance= 11R/20 here R=2. hence equivalent R=1.1 ohm. This was so simple.
     
  14. Jan 3, 2016 #13
    But the critical part may be how you will find the final equation.But it is easy too.
     
  15. Jan 3, 2016 #14
  16. Jan 3, 2016 #15

    cnh1995

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    Yes. That's what I got using delta-wye transform. Good job!
     
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