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