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)                 4 R                         

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 resistance.                 \[R'=\frac{\frac{R}{2}\times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{\frac{{{R}^{2}}}{4}}{R}=\frac{R}{4}\]