Equivalent resistance across a circuit made of 12 resistors

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Homework Help Overview

The discussion revolves around finding the equivalent resistance in a circuit composed of 12 resistors, with particular focus on symmetrical and asymmetrical configurations. Participants explore the implications of symmetry on current distribution and resistance calculations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the identification of symmetrical points in the circuit and how this affects current flow. There are attempts to simplify the circuit by ignoring certain resistors based on symmetry. Questions arise regarding the approach to take if the circuit lacks symmetry, particularly in calculating equivalent resistance between different points.

Discussion Status

Some participants have reached a numerical result for the equivalent resistance in a symmetrical case, while others express uncertainty about handling asymmetrical circuits. Suggestions for using Kirchhoff's Laws to set up equations for non-symmetrical configurations have been introduced, indicating a productive direction in the discussion.

Contextual Notes

Participants are navigating the complexities of symmetrical versus asymmetrical circuits, with specific reference to bridge-type circuits and their typical applications. There is an acknowledgment of the challenges posed by non-balanced configurations.

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hey can anybody please tell me how to solve this circuit?? :confused:

I tried this sum out but I can't understand which points are symmetrical and have same potential..or how the current is distributed
 

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The symmetry means that potential at C=D=E=F = 0.5 the pd between A and H
This means there is no current through the arms CD and FG. So you can ignore the 2 resistors there.
This allows you to simplify the circuit using series and parallel resistors.
 
ok, I solved the combinations and I got 3/4 R.
but what if the circuit is not symmetrical..that is if we have to find the equivalent resistance between A and B?
 
I also get 3/4 R.
If the circuit is not balanced, I can't see much use for it! Usually, these "bridge" type circuits are only useful when balanced. [eg Wheatstone bridge]

To attempt to answer the question, though, one possibility would be to set up a system of Kirchhoff's Law equations for the various closed loops (where ΣIR = 0) as well as the main circuit supplying the pd that provides the main current.
You would get 6 equations with 6 unknowns and a relationship between the main current and the applied pd. This would give the equivalent R.
 

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