Effective resistance between two points using symmetry

[Girish285]

Point D and C are equipotrntial so you can remove wire DC and see how the circuit look like

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[Girish285]

Thanks for replying .

This is exactly what I would like to understand [emoji2] .

Please assume this is a 2D circuit .

If I draw a line perpendicular to AB , the left and right parts are mirror image , this make points D and C symmetric . But symmetric points do not necessarily have to be equipotential . Right ?

How can then we argue that points C and D are equipotential .

Path symmetry indicates that D and C are equipotential

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[BvU]

Thanks !

Hello again,

I kept quiet because I was obviously making it worse for you in your frustration -- but I couldn't think of a good way to help you out without giving it all away. The picture I had in mind was, of course

and once you have it in front of you like this, the path is clear (thanks to the fact that all four on the right have the same resistancce)

(note: in many cases you can't even get it as 'flat' as this and there are one or more crossovers left to make life edifficult)​

and now I have a question for you:

with hindsight, what would have been a good hint that could have helped you effectively at that point ? (after all, you will definitiely not be the last one to get stuck with a problem like this).and as a side note: you see that I don't agree with

The original circuit cannot be drawn in-plane

 

[Jahnavi]

Hi BvU ,

and now I have a question for you:

with hindsight, what would have been a good hint that could have helped you effectively at that point ?

Not hint , but if you could have been a little more expressive and had written - "Please try my suggestion and you would clearly see how the two points C and D are equipotential using the same technique (drawing a line perpendicular to AB) you are trying to employ in the OP " . That would have worked

AND you could have added a smiley in post#6 .

I was under the impression that you had overlooked my concern in the OP and were trying to suggest an alternative strategy to simplify the circuit .

By no means this is an excuse .I was clearly wrong in not working as per your suggestion .

But then , this is the limitation with any online platform . It doesn't precisely portray your thinking/feeling .

 

[BvU]

Thanks, will more often !

 

[Jahnavi]

@BvU ,

I have posted another question here https://www.physicsforums.com/threads/equivalent-resistance-between-two-points.944478/ .

The problem is solved . But I am still not very confident about exploiting symmetries and arguing which points are equipotential. If you have some insight in that problem or would like to share your reasoning as to how you would tackle that problem , please do so .

Thanks !