question_answer

A wire has linear resistance \[\rho \](in Ohm/m). Find the resistance R between points A and B if the side of the larger square is 'd'.       

A) \[\rho d/\sqrt{2}\]           

B) \[\sqrt{2}\rho d\]

C) \[2rd\]               

D) None of these

Correct Answer: A

Solution :

[a] Let each half side has resistance \[r\left( =\rho d/2 \right)\] \[\therefore R=\frac{1}{2}\left[ 2r+\frac{\left( 2r \right)\left( r\sqrt{2} \right)}{\left( 2+\sqrt{2} \right)r} \right]=r\sqrt{2}\] (on solving) \[\therefore R=\rho d/\sqrt{2}\]