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

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

Updated On: Jun 23, 2023
  • R4 \frac{R}{4}
  • R8 \frac{R}{8}
  • 4R 4R
  • R2 \frac{R}{2}
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The Correct Option is A

Solution and Explanation

When wire is bent to form a complete circle then
2πr=R 2\,\pi r=R
r=R2π \Rightarrow r=\frac{R}{2\pi }


Resistance of each semicircle
=πr=πR2π=R2=\pi r=\frac{\pi R}{2 \pi}=\frac{R}{2}
Thus, net resistance in parallel combination of two semicircular resistances
R=R2×R2R2+R2=R24R=R4R'=\frac{\frac{R}{2} \times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{\frac{R^{2}}{4}}{R}=\frac{R}{4}
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