It takes 12 minutes to boil 1 litre of water | vedclass

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Question

(A) The heat required to boil $1$ litre of water is constant, $H$. The heat generated by an electric kettle is given by $H = \frac{V^2}{R}t$, where $V

Vedclass · Accepted Answer

$9.6$ minutes

Vedclass · Answer

(A) The heat required to boil $1$ litre of water is constant, $H$. The heat generated by an electric kettle is given by $H = \frac{V^2}{R}t$, where $V$ is the voltage, $R$ is the resistance, and $t$ is the time.Since $V$ is constant, $H \propto \frac{t}{R}$.Initially, $H = \frac{V^2}{R} 	imes 12$.The resistance of a coil is proportional to the number of turns $(N)$, so $R \propto N$.If $20\%$ of the turns are removed, the new number of turns is $N' = N - 0.2N = 0.8N$.Thus, the new resistance is $R' = 0.8R$.For the same amount of heat $H$, we have $\frac{V^2}{R} 	imes 12 = \frac{V^2}{R'} 	imes t'$.Substituting $R' = 0.8R$, we get $\frac{V^2}{R} 	imes 12 = \frac{V^2}{0.8R} 	imes t'$.$t' = 12 	imes 0.8 = 9.6$ minutes.

It takes $12$ minutes to boil $1$ litre of water in an electric kettle. Due to some defect, it becomes necessary to remove $20\%$ of the turns of the heating coil of the kettle. After repair, how much time will it take to boil $1$ litre of water?

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