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I found this while studying about the symmetry method of determining equivalent resistance. But, I cannot understand on what basis they are coming into this conclusion; how they are calling these points equipotential: enter image description here

A little bit elaboration on equipotential lines and symmetry method of Circuit Analysis will be very helpful.

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  • $\begingroup$ It is symmetrical so any current will split nicely between the 2 paths; i.e. current at A will split equally to B and C. $\endgroup$
    – QuIcKmAtHs
    Commented Jan 2, 2018 at 14:19
  • $\begingroup$ @XcoderX actually, my concept about equipotential lines and points is not clear. Can you please elaborate a little please? And how is the line of symmetry and equipotential points related? $\endgroup$
    – DJ Koustav
    Commented Jan 2, 2018 at 14:23
  • $\begingroup$ Hmm... basically the line of symmetry tells you that resistance on both sides are equal. Since current splits inversely to the ratio, but here, the ratio is 1:1, so current splits 1:1. This means that the same amount of current goes to both sides, so they are equipotential. My explanation here probably doesn't sound very "sciency", but I hope it is understandable. $\endgroup$
    – QuIcKmAtHs
    Commented Jan 2, 2018 at 14:26
  • $\begingroup$ @XcoderX Thanks, my concept is getting clear. I think some more problem solving would give me a proper hold on the topic. $\endgroup$
    – DJ Koustav
    Commented Jan 2, 2018 at 14:28
  • $\begingroup$ Perhaps you could upvote and check if it helps. $\endgroup$
    – QuIcKmAtHs
    Commented Jan 2, 2018 at 14:30

2 Answers 2

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Basically the line of symmetry tells you that resistance on both sides are equal. Since current splits inversely to the ratio, but here, the ratio is 1:1, so current splits 1:1. This means that the same amount of current goes to both sides, so they are equipotential. My explanation here probably doesn't sound very "sciency", but I hope it is understandable. There is a rule of thumb when solving circuits problem, which is to look for the line of symmetry, which can help simplify a complcated circuit(as shown in your post).

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  • $\begingroup$ One more thing please..... What's the rule of thumb? $\endgroup$
    – DJ Koustav
    Commented Jan 2, 2018 at 14:32
  • $\begingroup$ Isn't it said in the post. You kind of look for a line of symmetry, which is similar to the picture you posted @user29674 $\endgroup$
    – QuIcKmAtHs
    Commented Jan 2, 2018 at 14:33
  • $\begingroup$ O...I understand. I upvoted your answer but it is not shown up as my reputation is less than 15. $\endgroup$
    – DJ Koustav
    Commented Jan 2, 2018 at 14:35
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I believe that the voltage is applied across AD in the question. If you'd notice, the resistance between AB and AC are equal and so is the case for DE. and DF. When current flows through those particular branches, say AB and AC, the potential drop is the same due to symmetry and equal resistance. Hence the potential at points B and C are equal. Similarly the potentials at E & F are equal. This will help simplifying the circuit to a great extent.

Hope it helps!!!!

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