Two wires $A$ and $B$ made of same material and having their lengths in the ratio $6 : 1$ are connected in series. The potential difference across the wires are $3\,V$ and $2\,V$ respectively. If $r_A$ and $r_B$ are the radii of $A$ and $B$ respectively, then $\frac{{{r_B}}}{{{r_A}}}$ is
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$\therefore \quad V \propto R$
$\frac{V_{A}}{V_{B}}=\frac{R_{A}}{R_{B}}=\frac{\ell_{A} / r_{A}^{2}}{\ell_{B} / r_{B}^{2}}$
$\Rightarrow \frac{\mathrm{r}_{\mathrm{B}}}{\mathrm{r}_{\mathrm{A}}}=\sqrt{\frac{\mathrm{V}_{\mathrm{A}} \ell_{\mathrm{B}}}{\mathrm{V}_{\mathrm{B}} \ell_{\mathrm{A}}}}=\frac{1}{2}$
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