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Homework Help: Need help to find current in Y-delta (diamond-shaped) circuit

  1. Feb 7, 2013 #1
    1. The problem statement, all variables and given/known data
    where the voltage source given as 20V (forgot to add that in)
    Need to find the current I in the picture.

    2. Relevant equations
    equivalent resistance inside diamond is 2 pair resistors in series, put in parallel next.

    3. The attempt at a solution
    brought out the 20V voltage source inside the two diamonds outside, formed a rectangular circuit with both diamonds on the right side with 12ohms on all sides, and the 4ohm resistor still stuck in the center. brought out the 4ohm resistor using delta->Y transformation, however it is now 5.14ohm (12x12/12+12+4). this leaves 1.7ohm for the top two resistors on the inner diamond (12x4/12+12+4).

    combining series & parallel for inner diamond now:
    13.7 resistors both in parallel, so 6.85ohms brought out of the diamond next to the 5.14ohm one.

    now working with the outer diamond, the only one left:
    24ohm resistors both in parallel, 12ohms and bring this out finally and combine the in-series resistors into equivalent one:

    12+6.85+5.14=23.99 ohms, so current I is 20V/23.99ohm=0.83A. but have a feeling i did this wrong...
  2. jcsd
  3. Feb 7, 2013 #2
    There is no need to apply Y-delta transform. The circuit can be transformed as shown in the attachment. The blue boxes represent 12 ohm resistors.

    Attached Files:

  4. Feb 8, 2013 #3
    hmm...are you sure about that? in my book it says if there's a resistor in the center of a diamond, you should apply the Y-delta transformation. but if your right, then that makes this a LOT simpler.

    anyway this is what i got when i reworked it:
    eq. resistance from each diamond: (24x24/24+24)=12ohm.
    resistance of circuit = 4ohm+2*12ohm=28ohm
    current I=20V/28ohm=0.71A

    hmm..not a lot of difference from my original answer. but is this right?
    Last edited: Feb 8, 2013
  5. Feb 8, 2013 #4
    Nope, it doesn't matter where you place it.

    Check your value of equivalent resistance again.
  6. Feb 8, 2013 #5
    i got it. placed the two equivalent resistances from the 2 diamonds in parallel with each other. 12ohms || 12ohms = 6ohms.


    this answer is right?
  7. Feb 8, 2013 #6
    Yep, that's what I got.
  8. Feb 8, 2013 #7
    I missed this. Use Y-delta transform only when you find no other way. I myself hate this transformation when the resistors are of different values. It leads to some ugly calculations. Try to see if you can reduce the circuit before using the transformation. Like in this question, if you had look around instead of following the book, you surely would have solved it.
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