question_answer

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

A) \[\frac{R}{4}\]       

B)                                        \[\frac{R}{8}\]                  

C) \[4R\]                   

D)        \[\frac{R}{2}\]

Correct Answer: A

Solution :

When wire is bent to form a complete circle then \[2\pi r=R\] \[\Rightarrow \]               \[r=\frac{R}{2\pi }\] Resistance of each semicircle \[=\pi r=\frac{\pi R}{2\pi }=\frac{R}{2}\] Thus, net resistance in parallel combination of two semicircular resistances \[R=\frac{\frac{R}{2}\times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{\frac{{{R}^{2}}}{4}}{R}=\frac{R}{4}\]