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(C) When a wire of total resistance $R = 12\,\Omega$ is bent into a circle,the wire is divided into two equal halves by any diameter.Each half of the

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$3$

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(C) When a wire of total resistance $R = 12\,\Omega$ is bent into a circle,the wire is divided into two equal halves by any diameter.Each half of the wire will have a resistance of $R' = \frac{R}{2} = \frac{12}{2} = 6\,\Omega$.These two halves are connected in parallel between the two points on the diameter.The equivalent resistance $R_{eq}$ of two resistors $R_1$ and $R_2$ in parallel is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$.Here,$R_1 = 6\,\Omega$ and $R_2 = 6\,\Omega$.Therefore,$\frac{1}{R_{eq}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$.Thus,$R_{eq} = 3\,\Omega$.

$A$ wire has resistance $12\,\Omega$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to ................ $\Omega$.

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