The property of a conductor which tends to restrict the flow of current through the conductor is called resistance.
SI unit of resistance is ohm ( $\mathit{\Omega }$ ). When a potential difference of $1\mathrm{V}$ applied across a wire gives rise to $1\mathrm{A}$ of current through the wire, then the resistance is said to be $1\mathrm{ohm}$ $\left(1\mathit{\Omega }\right)$.
The resistance of conductor depends on length, thickness, nature of material and temperature of conductor.
(i) If the length is doubled, then $\mathrm{R}$ is doubled because the resistance of a conductor is directly proportional to length i.e., $\mathrm{R}\propto \mathit{l}$.
(ii) Resistance of a conductor is inversely proportional to the square of its diameter or area of cross-section. So, if the radius of conductor is doubled, its resistance becomes one-fourth.
i.e., $\mathrm{R}\propto \frac{1}{\mathrm{A}}$
and
$\mathrm{A}=\mathit{\pi }{\mathit{r}}^2$
If
${\mathit{r}}^{\prime }=2\mathit{r}$, then
${\mathrm{A}}^{\prime }=\mathit{\pi }{\mathit{r}}^2=\mathit{\pi }{\left(2\mathit{r}\right)}^2=4\mathit{\pi }{\mathit{r}}^2=4\mathrm{A}$
If ${\mathrm{A}}^{\prime }=4\mathrm{A}$, then
${\mathrm{R}}^{\prime }=\mathit{\rho }\frac{{\mathit{l}}^{\prime }}{{\mathrm{A}}^{\prime }}=\mathit{\rho }\frac{\mathit{l}}{4\mathrm{A}}=\frac{1}{4}\left(\mathit{\rho }\frac{\mathit{l}}{\mathrm{A}}\right)$
$=\frac{1}{4}\mathrm{R}$
Therefore, if radius is doubled, the resistance becomes one fourth.