A cylindrical conductor of length 'l' and uniform area of cross section ' $A$ ' has resistance ' $R$

Question

A cylindrical conductor of length 'l' and uniform area of cross section ' $A$ ' has resistance ' $R$ '. The area of cross section of another conductor of same material and same resistance but of length ' $2 l$ ' is\

Professor PC Thomas Classes · Answer

(c) : The resistance of a conductor of length I, and area of cross section, \ $A$ is  R=$ho=\frac{l}{A}$ \ where, $ho$ is the resistivity of the material.
Now for the conductor of length $2 l$, area of cross-section $A^{\prime}$ and resistivity $ho$.$$
R^{\prime}=ho \frac{I^{\prime}}{A^{\prime}}=ho \frac{21}{A^{\prime}}$$
But given, $R=R^{\prime} \Rightarrow ho \frac{1}{\mathrm{~A}}=ho \frac{21}{\mathrm{~A}^{\prime}}$\
or $A^{\prime}=2 A$
\Shortcuts  - Resistivity, $ho \propto R, A$ and $ho=\frac{1}{1}$