Water boils in an electric kettle in $20$ minutes after being switched on. Using the same main supply, the length of the heating element should be. . . . . . .to . . . . . .. times of its initial length if the water is to be boiled in $15$ minutes.
JEE MAIN 2024, Diffcult
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$\mathrm{P}=\frac{\mathrm{v}^2}{\mathrm{R}}, \mathrm{R}=\frac{\rho \ell}{\mathrm{A}}$
$\mathrm{P} \propto \frac{1}{\ell}$
$\frac{\mathrm{P}_1}{\mathrm{P}_2}=\frac{\mathrm{t}_2}{\mathrm{t}_1}=\frac{15}{20}=\frac{\ell_2}{\ell_1}$
$\ell_2=\frac{3}{4} \ell_1$
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