How to find the equivalent resistance using symmetry

circuit analysisresistance

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I know this could be solved using delta-to-y transformation, but I want to solve this using symmetry.

Considering the middle line the symmetry axis this becomes:


simulate this circuit – Schematic created using CircuitLab

Then, you see the we have the equivalent resistance: (1 + 0.5 + 0.5) + (0.5) = 2.5 ohms.

What's the problem?

Best Answer

If you draw it a bit different, it's easy to see that there is no current flowing through the middle resistor. (It's a bridge with equal R's in all the arms.) So you can remove the central R from the circuit. From there it's easy.

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