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Finding Req - Understanding Professor's Solution

  1. Sep 25, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-9-25_14-53-41.png

    2. Relevant equations
    Series: Req = r1 + r2...
    Parallel: 1/req = 1/r1 + 1/r2...

    3. The attempt at a solution
    upload_2016-9-25_14-53-26.png
    This is my professors solution for the problem and of course without any explanation it doesn't make sense to me. Under what principle can he justify immediately adding 10 + 8?

    upload_2016-9-25_14-56-38.png
    For my solution I redrew the circuit and did:
    5||20 = 4
    10+4 = 14

    3 || 6 = 2
    2+8 = 10

    10+14 = 24

    Another question: Had I not redrawn the circuit I still would've gotten 14 and 10 but I would've thought they would be in parallel with each other with the way its drawn out?

    I understand redrawing it is the easiest way to make sure I have it correct but there won't be enough time unless I immediately recognize what it looks like.
     

    Attached Files:

  2. jcsd
  3. Sep 25, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Is there any path that you can draw between a and b (following circuit pathways of course) that does not pass through both the 10 and 8 Ohm resistors? If not, they must be in series between a and b.

    The trick is to look at the nodes that are bridged by a short circuit. In this circuit nodes c and f are connected together via a wire. That means you are free to move all the connections at one of those nodes to the other node. Symmetry also helps here, as you can put nodes c and f together by "folding" the circuit along a line passing through d-a-b-e. Once you make that fold you've got your parallel resistor connections that you and your professor found, while the two series resistors are left at the fold.
     
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