Thirteen Resistances Each Of Resistance R Omega Are Connected In The Circuit. What Will Be The Effective Resistance Between A And B?

The potential difference across the central resistor is zero due to symmetry of the circuit.

The resistor is the equivalent resistor of the small triangle configuration at the four corners.

The effective resistance is the same as the resistance of a single unit triangle shaped resistance.

Hence, effective resistance =\( \frac{(R+R)*(R)}{(R+R)+(R)} = \frac{2R}{3}\)

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