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