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(C) When a wire of resistance $R = 12 \,\Omega$ is bent into a circle,the resistance is distributed uniformly along the circumference.When we consider

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(C) When a wire of resistance $R = 12 \,\Omega$ is bent into a circle,the resistance is distributed uniformly along the circumference.When we consider two diametrically opposite points,the circle is divided into two equal semicircular parts.The resistance of each semicircular part is $R' = \frac{R}{2} = \frac{12}{2} = 6 \,\Omega$.These two semicircular parts are connected in parallel between the diametrically opposite points.The equivalent resistance $R_{eq}$ is given by the formula for two resistors in parallel:$\frac{1}{R_{eq}} = \frac{1}{R'} + \frac{1}{R'} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$.Therefore,$R_{eq} = 3 \,\Omega$.

$A$ wire of resistance $12 \,\Omega$ is bent into a circle. What is the equivalent resistance between two diametrically opposite points in $\Omega$?

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