Water boils in an electric kettle in 20 minutes after being...

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.

Options

Adecreased, $3 / 4$
Bincreased, $4 / 3$
Cdecreased, 4/3
Dincreased, $3 / 4$

Correct answer

A. decreased, $3 / 4$

Step-by-step solution

\begin{aligned} & \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\end{aligned}

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