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Circuit Simplification (Equivalent Resistance)

  1. Aug 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine the equivalent resistance of this circuit.

    http://img444.imageshack.us/img444/5137/19910965.png [Broken]

    3. The attempt at a solution

    So I realize that both of the 6 ohm resistors on each side are in series with each other. However, I am stuck after that part since I do not recognize a series or parallel connection from that point onwards. This is really in part due to the empty stretch of wire connecting the left and right vertical wires to the middle two wires. There are obviously no other resistors the 12 ohm equivalent resistors can connect to; there are also no two nodes that are shared by the 12 ohm equivalent resistor and another resistor.

    Any clue as to how to proceed would be greatly appreciated.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Aug 26, 2012 #2
    There are 2 vertical shorted connections.
    You can see it clearer if you reduce each lenght until it becomes a point.
     
  4. Aug 26, 2012 #3
    Right so I got an answer of 4 ohms as the equivalent resistance. Anyone concur?
     
  5. Aug 26, 2012 #4
    Can you show your working.
     
  6. Aug 26, 2012 #5
    Right, so first I combined the 6ohm resistors on each side into 12 ohm resistors. Then I redrew the circuit into deltas/triangles. This allowed me to find Rab by taking the 12 ohm on the right in parallel with the 6 ohm on the bottom half of the midsection. Then I took that equivalent resistor in series with the 14 ohm resistor. Then I took that entire equivalent resistor computed so far in parallel with the 9 ohm resistor and also (12 ohm left resistor in parallel with the 12 ohm top midsection resistor and then that equivalence in series with the top 6 ohm resistor).
     
  7. Aug 26, 2012 #6
  8. Aug 26, 2012 #7
    As your answer.
    1/Rt=1/12 +1/12+1/12
     
  9. Aug 26, 2012 #8
    Ok thanks, so I did get the right answer but did I solve it wrong?
     
  10. Aug 26, 2012 #9

    lewando

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    Gold Member

    Re: Equivalent Resistance Problem

    Not sure what you mean by "delta configs". If you collapse the wires connecting the central 9-ohm to the upper 6-ohm and lower 14-ohm, it becomes more readable as a straightforward parallel-series reduction. 4-ohms looks right.
     
  11. Aug 26, 2012 #10

    CWatters

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    Science Advisor
    Homework Helper

    Re: Equivalent Resistance Problem

    Try looking at it like this Then start on the right hand side.
     

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