Wye-Delta Transforms?

Discussion in 'Homework Help' started by Sgt.Incontro, Dec 1, 2013.

  1. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
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    Hi,

    The question says:

    Find a equivalent Pi network for the network below:

    [​IMG]

    My attempt at a solution:
    For the equivalent pi circuit seen on this webpage (purely for convenience), I get:

    R2 = 2.997
    R1 = 3.136

    Are these answers correct? If not, then I am happy to run through my full attempt, but I hope my answers are correct.

    Thanks :)
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    If you would kindly show your working, your method can be checked as to why you arrived at what appear to be incorrect answers.
     
  3. WBahn

    Moderator

    Mar 31, 2012
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    Always ask if your answer makes sense.

    Notice the symmetry here. You can call any terminal in the original schematic as being any terminal in the pi-network schematic. This requires that that R1=R2, doesn't it?
     
  4. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
    50
    1
    So my answer is definitely wrong then?

    If that is the case, I have no choice but to probably upload ALL the pages in my solution.
     
  5. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
    50
    1
    Perhaps, though I'm not entirely sure.

    So are you also saying as the other posted did, that my solution is incorrect?

    Bugger. I will upload my solution then.
     
  6. WBahn

    Moderator

    Mar 31, 2012
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    It shouldn't take very many lines to get the solution. But go ahead and post your work. We might suggest immediately a different way of going about the analysis, but can't really do that until we see what you did.
     
  7. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
    50
    1
    Last edited: Dec 2, 2013
  8. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
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    Sol. posted. Thanks.

    Edit: Sorry if it's a little messy.
     
  9. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,805
    While the approach you are taking looks valid (my guess is that you've made a math error some place), you are making it a LOT harder than it needs to be.

    You clearly know that transforming a symmetric wye into a symmetric delta, or vice-versa, involves just a factor of three. See if you can solve it without ever transforming anything other than symmetric wyes and deltas.
     
  10. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
    50
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    Hmm, I don't know, but I will check for math errors at first then.

    I will also try this.

    Any other tips for the meantime? More importantly, am I actually ALLOWED to cancel the two resistors on each side, due to the fact they are parallel? I am talking about resistor RAB ||1ohm, and Rbc||1ohm... (top of page 3 of my document)
     
  11. WBahn

    Moderator

    Mar 31, 2012
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    What does it mean to "cancel" two resistors?

    On what basis do you consider (Rab||1Ω) to be in parallel with (Rbc||1Ω)? What is required for two resistors to be in parallel?
     
  12. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
    50
    1

    By cancel, I meant simplify.

    And sorry if I explained it badly, I didn't mean that way.

    I meant this: (image grabbed from page 3 of my solutions)

    https://copy.com/lTNEaO7cS7BDX4FU

    Does that make more sense?
     
  13. WBahn

    Moderator

    Mar 31, 2012
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    I agree that Rab is in parallel with a 1Ω resistor and can be combined with it. Likewise for Rbc and the 1Ω resistor it is in parallel with. But that's all the further it goes.
     
  14. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
    50
    1
    Ok, I tried approaching the question differently, trying to make sure that each stage of the problem, the remaining unsolved network remains SYMMETRICAL.

    On my second attempt, I got R (all three) to be = 19/5 ohms.

    Is this possibly correct?
     
    Last edited: Dec 2, 2013
  15. Sgt.Incontro

    Thread Starter Member

    Dec 5, 2012
    50
    1
    I think this answer may be correct.

    Thanks everyone for the help.
     
  16. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    This wasn't my answer. I'll re-check my values in any case.

    However, looking at the original schematic there's no way the resistance between any two terminals could be twice 19/5 or 7.6 ohms.

    Sorry, I was thinking of a T network rather than the PI network. You are correct.
     
    Last edited: Dec 2, 2013
  17. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,805
    This is correct.

    As a sanity check, look at the original circuit. Do you see that the resistance between any pair of terminals, with the other one left flowing, has to be somewhere between 2Ω and 3Ω?

    With 19/5 Ω, the resistance is (19/5)(1Ω||2Ω) = (19*2)Ω/(5*3) = 38/15 Ω which is basically 2.5Ω.
     
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