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How can I use the symmetry for solving problems in equivalent resistance for a given complicated mesh. Are there any sort of rules for this purpose? Please explain with some examples.Thank you.

How can I use the symmetry for solving problems in equivalent resistance for a given complicated mesh. Are there any sort of rules for this purpose? Please explain with some examples.Thank you.

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
The symmetry of the equivalent resistor systems we examined takes into account a shrewd improvement of the issue of ascertaining the compelling resistances. The thought, presented by van Steenwijk] is to show the system when a present I is passed into one hub and a current of I/(H −1) is taken out through the rest of the H − 1 hubs. We at that point comprehend that framework for the streams through all edges and superimpose it on a similar system with all ebbs and flows invalidated and turned to such an extent that the present I now leaves a hub of intrigue. The superimposed framework will be one in which current HI/(H − 1) enters one hub and leaves another, and zero current enters or leaves each other hub. This approach has two noteworthy advantages. Initially, since our superimposed framework comprises of two systems varying just by revolution, we require just illuminate the first arrangement of conditions once to acquire the resistance between any two hubs in the system. Second, we can take a gander at the system as having layers of symmetrically equal hubs. Each of the symmetrically proportional hubs will offer ascent to indistinguishable circuit conditions, so it suffices to consider only a solitary hub from a layer in setting up the conditions. This prompts a noteworthy decrease in the quantity of conditions that must be explained .

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