It takes 15 min to heat water in an electric | vedclass

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(C) The heat produced $H$ is given by the formula $H = \frac{V^2 t}{R}$,where $V$ is the voltage,$t$ is the time,and $R$ is the resistance of the coil

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$10$

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(C) The heat produced $H$ is given by the formula $H = \frac{V^2 t}{R}$,where $V$ is the voltage,$t$ is the time,and $R$ is the resistance of the coil.Since the same amount of water is heated,$H$ remains constant. Also,the voltage $V$ is constant.Therefore,$t \propto R$.The resistance $R$ is given by $R = ho \frac{l}{A}$,where $ho$ is resistivity,$l$ is length,and $A$ is the cross-sectional area.Thus,$t \propto l$.Given $l_2 = \frac{2}{3} l_1$ and $t_1 = 15 \ min$.Using the ratio $\frac{t_2}{t_1} = \frac{l_2}{l_1}$,we get $\frac{t_2}{15} = \frac{2/3 l_1}{l_1}$.$t_2 = 15 	imes \frac{2}{3} = 10 \ min$.

It takes $15 \ min$ to heat water in an electric kettle. If the length of the heating coil is reduced to $2/3$ of its original length,how many minutes will it take to heat the same amount of water?

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