Equivalent resistance of this 6-sided circuit

AI Thread Summary
The discussion focuses on determining the equivalent resistance of a six-sided circuit using symmetry arguments. Participants explore the relationship between currents in resistors connected to a central node, concluding that currents through symmetrical resistors are equal, allowing for simplifications without removing resistors. They discuss how to split the central node into two to analyze the circuit more effectively, leading to calculations of equivalent resistances. The conversation highlights the importance of understanding current flow and symmetry in circuit analysis. Ultimately, the participants aim to simplify the circuit to find the equivalent resistance accurately.
  • #51
Sat-P said:
Got it
So can you solve it now using the splitting up of node 0?
 
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  • #52
Even after I split the node 0ab , the other radial resistors are causing me trouble, if I can get a way to simplify them then it will be all good
 
  • #53
Sat-P said:
Even after I split the node 0ab , the other radial resistors are causing me trouble, if I can get a way to simplify them then it will be all good
In post #32 you recognised (guessed?) that, by symmetry, the current along 2-0 is the same as along 0-5. That allows you to split ##0_{2345}## into two nodes, ##0_{25}, 0_{34}##.
 
  • #54
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Once you understand the consequences of the dashed red symmetry line, you can work from right to left.

##\ ##
 
  • #55
Sir, I've tried both the methods you gave
The answers I am getting are different, please check is there something I did wrong or misinterpreted what you said

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1721564378304636417938574175375.jpg
 
  • #56
What are we looking at ? (with a pain from craning our neck) ?
I can distinguish you replace the rightmost three with ##{2\over 3} R##, so the rightmost five give ##{8\over 3} R##. OK.

But why ##R/2## ?

1721576599814.png


##\ ##
 
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  • #57
Oh, I just saw the mistake. Let me do it again
 
  • #58
After solving this one I got 11R/20 so is it the answer, did I do it right
 
  • #59
Sat-P said:
After solving this one I got 11R/20 so is it the answer, did I do it right
Agrees with mine, but I didn't double check.

Checking your own work is a key skill in the physical sciences. Out in the real world they don't want to pay 2 people to do one job, and they don't want to pay one person to do the job incorrectly.
 
  • #60
Sat-P said:
After solving this one I got 11R/20 so is it the answer, did I do it right
The answer isn't really the important element. Whther you did it right can only be confirmed if you post your work.

Free tip: work it out neatly ... :wink:

1721594406599.png
 
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