Question

A uniform wire of resistance $R$, of the radius $r$ is uniformly drawn until its radius is reduced to $r/ n$, Its new resistance is

• A. $n R $
• B. $n^3 R $
• C. $n^2 R $
• D. $n^4 R $

Answer 1

Answer: (D)

Here, $R = \frac{\rho l}{A} = \frac{\rho l}{\pi r^2}$
As, $r' = \frac{r}{n} , l' = ?$
or, $r^2 l = \left( \frac{r}{n} \right)^2 l'$
or, $l' = n^2 l $
New resistance of the wire, $R' = \frac{\rho l'}{A'} = \frac{ \rho l'}{\pi r'^2}$
or , $R' = \frac{\rho}{\pi} \times \frac{n^2 l }{( r / n)^2} = n^4 \frac{\rho l}{\pi r^2} = n^4 R $