Two wires of the same material and having lengths in the ratio of 2 : 3 are connected in series. The p.d.s across the wires are 4.2 V and 3.6 V respectively. Compare their radii.

Since the wires are in series current flowing through the wires will be equal

According to ohm's law $\mathrm{V}=\mathrm{iR}\Rightarrow \mathrm{V}=\frac{\mathrm{i}\times \mathrm{\rho l}}{\mathrm{A}}$

$4.2=\frac{{\mathrm{P\rho l}}_1}{{\mathrm{\pi r}}_1^2}\to \text{ (i) }$

$\text{ 3. }6=\frac{{\mathrm{i\rho l}}_2}{{\mathrm{\pi r}}_2^2}\to \text{ (ii) }$

$\frac{\left(1\right)}{\left(2\right)}=\frac{4.2}{3.6}=\frac{7}{6}=\left(\frac{{\mathrm{l}}_1}{{\mathrm{l}}_2}\right)\times \frac{{\mathrm{r}}_2^2}{{\mathrm{r}}_1^2}$

${\mathrm{r}}_1:{\mathrm{r}}_2=2:\sqrt{7}$