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A wire has linear resistance \rho (in~ \Omega / \mathrm{m} ). Find the resistance R between points A and B if the side of the big square isd.


 

Option: 1

\mathrm{\frac{\rho d}{\sqrt{2}}}


Option: 2

\mathrm{\sqrt{2 \rho d}}


Option: 3

\mathrm{2 \rho d }


Option: 4

None of these


Answers (1)

best_answer

The circuit is equivalent to


Let each half side has resistance \mathrm{\frac{\rho r d }{2}}


On solving, we get

\begin{aligned} &\mathrm{ R=\frac{1}{2}\left[2 r+\frac{(2 r(r \sqrt{2}))}{(2+\sqrt{2}) r}\right]=r \sqrt{2} }\\ &\mathrm{ =\frac{\rho d}{\sqrt{2}} }\end{aligned}

Posted by

Irshad Anwar

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