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My teacher had taught us how to solve circuit problems using symmetry. One of the symmetry axis he had called "transverse symmetry" which the axis will be perpendicular to the line joining the terminals , he said without proving that in a branch of the circuit the current will be equal in it's mirror image. This did not seem so obvious to me.

Can this be proven or convincingly shown?

Qmechanic
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Glowingbluejuicebox
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1 Answers1

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Now that you seems to have answered your own question, I will just summary it here.

The sole parameter for symmetry in a circuit is when current on the two branches are the same. Don't be under the impression that the look of the circuit is what makes it symmetric. "Looks can be utterly deceptive."

Now, Current in two branches is same when -
i. two branches have identical resistance and potential difference OR
ii. $V_2$ and $R_2$ of the second branch is such that $$\frac{V_2}{R_2}=I=\frac{V_1}{R_1}$$ basically the Ohm's Law.

Now if this criteria is satisfied, you can name the various symmetries, by the "look" of the circuit.

TheImperfectCrazy
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