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:                                                                         [AIPMT (S) 2005]

A)  \[\frac{R}{4}\] 

B)                   \[\frac{R}{8}\]

C)  \[4\,R\]

D)                   \[\frac{R}{2}\]

Correct Answer: A

Solution :

[a] 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.

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