Potential of two points how are they same?

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The discussion revolves around understanding the concept of points at equal electrical potential in circuits with resistors. The user is confused about why points E, G, and D are at the same potential in one scenario, while points A, F, D, and G are considered equivalent in another. The explanation highlights that symmetrically equivalent points maintain equal potential due to their geometric arrangement. The user seeks clarification on the symmetry involved when a cell is connected between points A and B, and why current does not flow through certain points. The conversation emphasizes the importance of symmetry in determining electrical potential in circuit analysis.
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Homework Statement



I am confused here .
Each wire is of resistance R
How in this image

76xQa.png


E G and D are at the same potential

and in this image
pzhfZ.png

How A and F and Dand G are equivalent?

Homework Equations



I don't think any equations will be used in solving this but I guess V =IR might be

The Attempt at a Solution



In the first image what I figured out is since the points E G and D are at one resistor drop from H so they are at the same potential but I am not able to figure out in the second situation

I am taking help of this website
http://physicstasks.eu/uloha.php?uloha=285
but its quiet confusing
I JUST WANTED TO KNOW WHATS THE METHOD BEHIND FINDING POINTS WITH EQUAL POTENTIAL IN SUCH CASES ?
 
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Symmetrically equivalent points are at equal potential. Those points are equivalent which transform into each other during a symmetry operation.
Have you got a cube? Turning it around the body diagonal HB by 120° would not change anything: It looks the same as before. If you connect the battery to the points H and B, on the same axes, nothing happens again as the battery transforms into itself.
In the other case, the battery is in the mirror plane EHCB. The point A is mirror image of F, and D, G are also mirror images to each other, so they are equivalent.

ehild
 

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Thank you ! So much respect .
 
Just a little more help . Please explain what's up with this one
1rjNe.png

Where is the symmetry here if the Cell is connected btw A and B ?
Also in the second figure why doesn't current flow through FG and AD ?
 
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It is a mirror plane again...

ehild
 

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