Question

A certain piece of copper is to be shaped into a conductor of minimum resistance. Its length and diameter should be respectively

• A. $l,d$
• B. $2l,d$
• C. $\frac{l}{2},2d$
• D. $2l,\frac{d}{2}$

Answer 1

The correct option is C $\frac{l}{2},2d$

Since $R=\frac{\rho l}{A}=\frac{\rho l}{\pi (d/2{)}^2}=\frac{4\rho l}{\pi d^2}$

here $R$ is directly depend upon length and inversly depend upon diameter of conductor.
If $l$ becomes $\frac{l}{2}\&d$ becomes $2d,$ the new resistance is $R^{\prime }=\frac{\rho \frac{l}{2}}{\pi {\left(\frac{2d}{2}\right)}^2}=\frac{\rho l}{2\times \pi d^2}=\frac{R}{8}$
This is minimum among all the given instances.