It takes $12$ minutes to boil $1$ litre of water in an electric kettle. Due to some defect it becomes necessary to remove $20 \%$ turns of heating coil of the kettle. After repair, how much time will it take to boil $1$ litre of water.
AIIMS 2019, Diffcult
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The amount of heat generated is,
$H =\frac{ V ^{2}}{ R } t$ $....(i)$
It is given $20 \%$ heat is heat to be ejected, thus, the resistance is reduced by $20 \%$
The new resistance is,
$R ^{\prime}= R -0.2 R =0.8 R$
The new amount of heat generated is,
$H ^{\prime}=\frac{ V ^{2}}{0.8 R } t ^{\prime}$ $....(ii)$
On equating both equations $(i)$ and $(ii)$ we get,
$\frac{ V ^{2}}{ R } t =\frac{ V ^{2}}{0.8 R } t ^{\prime}$
$t ^{\prime}=0.8 \times t =0.8 \times 12 min =9.6 min$
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