Question

A wire has linear resistance $\rho$ (in $\Omega /m$). Find the resistance $R$ between points $A$ and $B$ if the side of the larger square is ${}^{\prime }{d}^{\prime }$.

• A. $\rho d/\sqrt{2}$
• B. $\sqrt{2}\rho d$
• C. $2\rho d$
• D. None of these

Answer 1

The correct option is A $\rho d/\sqrt{2}$

Let each half side has resistance $r(=\rho d/2)$

$\therefore$$\therefore R=\frac{1}{2}[2r+\frac{\left(2r\right)\left(r\sqrt{2}\right)}{(2+\sqrt{2})r}]=r\sqrt{2}$
(on solving)
$\therefore R=\rho d/\sqrt{2}$