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Method of Symmetry for Equivalent Resistances

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I have been studying the method of symmetry from some days, which essentially reduce the effort needed for the evaluation of equivalent resistances. My textbook states:

Points having symmetrically located about initial and final points have the same potentials.So, the resistances between these points can be ignored.
Understanding Physics, DC Pandey

Okay, fine. Problems get solved,but I have some questions regarding this.

  • Why does the method of symmetry work?
  • Does the method only apply for resistors of equal value/magnitude?
  • If yes, then how do we deal with asymmetrical circuit of resistors, say, in a cube?
  • And most essentially, how do we define symmetry?

Please help me. If you can, please recommend some JEE Physics Textbooks too.

Thanks!

Swapnil Das
 

CWatters

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Nodes that are at the same potential can be connected together without affecting the circuit. This then allows you to simplify the circuit using the rules for parallel and series components.
 
Nodes that are at the same potential can be connected together without affecting the circuit. This then allows you to simplify the circuit using the rules for parallel and series components.
But how does the method assume that they are at the same potential?
 

CWatters

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But how does the method assume that they are at the same potential?
Do you understand how a Potential Divider works?

What happens if you scale all the resistors in a Potential Divider circuit?
 
Do you understand how a Potential Divider works?

What happens if you scale all the resistors in a Potential Divider circuit?
Are they at the same potential? Is it the same principle out there?
 

CWatters

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Yes.
 

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