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I Finding equal potential points in electric circuits

  1. Mar 4, 2016 #1
    Hi! I have a real problem in understanding the use of symmetry for finding equal potential points in nasty electric circuits. There are lots of problems were the solution simply says: "due to symmetry reasons, nodes X and Y have equal potential", but I rarely really understand the so called symmetry. So far I haven't found someone to properly explain to me how this really works.

    To better explain myself, I annexed a cubic circuit. The problem asks to find the equivalent resistance when the circuit is connected to a voltage source between points S and A. The values for R1 and R2 are considered known. The solution says that the points I, M and the points H, B are at equal potential, so you can connect them together. Why those points?
    Bare in mind, this is no homework, just an example (though I would be grateful if anyone would help me understand it).

    So, can anyone explain me how to find symmetry in similar cases or suggest a paper on this topic?

    Attached Files:

  2. jcsd
  3. Mar 4, 2016 #2


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    Staff: Mentor

    You can quickly find candidates just by looking at the vertices, checking them is more work:
    Are there vertices with 3 R1? T and A, but as the voltage source is connected to A those are not at the same potential.
    Are there vertices with 2 R1 and 1 R2? I, M, B, H. Both I and M are connected to S via R2, both B and H are connected to A via R1. Possible candidates.
    Are there vertices with 1 R2 and 2 R2? No.
    Are there vertices with 3 R2? C and S. Same argument as with T and A: not at the same potential.

    Can I/M and B/H be pairs at the same potential?
    I is connected to S via R2, to T via R1, to H via R1.
    M is connected to S via R2, to T via R1, to B via R1. They are at the same potential if B and H are at the same potential.
    The same analysis for B/H shows that they are at the same potential if I and M are at the same potential. In other words, the points are symmetric, and at the same potential within the pairs.
  4. Mar 4, 2016 #3
    Thank you!This was really helpful and revealing.
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