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(B) Step $1$: Analyze the resistance of the segments.Since the wire is uniform,bending it into a circle divides the total resistance $R$ into two equa

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$R/4$

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(B) Step $1$: Analyze the resistance of the segments.Since the wire is uniform,bending it into a circle divides the total resistance $R$ into two equal halves of $R/2$ each,corresponding to the two semicircular arcs.Step $2$: Determine the circuit configuration.When considering two diametrically opposite points,these two semicircular segments are connected in parallel between these points.Step $3$: Calculate the equivalent resistance.The equivalent resistance $R_{eq}$ for two resistors $R_1$ and $R_2$ in parallel is given by $R_{eq} = \frac{R_1 R_2}{R_1 + R_2}$.Here,$R_1 = R/2$ and $R_2 = R/2$.$R_{eq} = \frac{(R/2) 	imes (R/2)}{(R/2) + (R/2)} = \frac{R^2/4}{R} = \frac{R}{4}$.Thus,the equivalent resistance between any two diametrically opposite points is $R/4$.

When a wire of uniform cross-section $a$,length $ℓ$,and resistance $R$ is bent into a complete circle,the resistance between any two diametrically opposite points will be .......

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