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## Homework Statement

Find the effective resistance between the points 'x' and 'y'. When the middle Resistance is 5 ohms.

## Homework Equations

Ohm's Law - V=IR. Kirchhoff's Junction and Loop (Mesh) Rule.

## The Attempt at a Solution

I drew the following diagram:

I got the correct answer when I took the loops 'ABCA' and 'ADBA' and resolved ##i_1## and ##i_2## (using Kirchhoff's Rules) in terms of ##i## and applied this into an imaginary loop which contains an arbitrary cell of emf ##V## (its terminals connected to 'x' and 'y') and finding ##R_{eq}=V/i##.

But when I tried doing this problem by taking the loops 'xADyx' (which contains an imaginary arbitrary cell) , then the loop 'xAByx' and then 'xCByx' and as above resolve ##i_1## and ##i_2## in terms of ##i## and when I find ##V/i## I get the wrong answer. I tried many times. Is there something I am doing wrong in the second case? Or am I repeatedly making algebraic mistakes?

One more question: My textbook resolves the above diagram using symmetry. In the text they take the current going through both the ##5\Omega## as same and similarly in both the ##10\Omega## resistors as same. How do they do that? How can I find symmetry in a circuit ?