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Generalized method for dealing with circuit involving symmetry?

Discussion in 'Physics' started by claws, Oct 8, 2018.

  1. claws

    claws Guest

    I'm a physics tutor for high school students. I'm finding it difficult to teach students how to exploit symmetry while finding equivalent resistance of a given network of resistors. I was Googling but couldn't find any generalized method that is applicable for any circuit with symmetry. The answers to How to find points with same potential while solving an equivalent resistance problem? also say that there isn't a generalized method.

    But I found this fantastic course handout of a Microwave Engineering course which tries to define symmetry mathematically using Group theory (I don't know group theory but the handout explained it in such a simple manner that even a lay person could understand).

    An example from the slide:


    I understood it till the 8th slide. Then it goes on to say:

    The importance of this can be seen when considering the scattering matrix, impedance matrix, or admittance matrix of these networks.

    I don't know what these matrices are. They seem to specific to Microwave Engineering.

    Question: How can the concepts developed in this presentation (up to slide 8) can be used for simple resistor circuits involving symmetry and find potentials, currents and equivalent resistances?

    To give a sense of the kind of symmetric circuits I'm dealing with, here are few circuits: [​IMG] [​IMG] [​IMG]

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