An electric kettle has two heating coils. When one of the coils is connected to an a.c. sotuce, the water in the kettle boils in $10$ minutes. When the other coil is used the w’ater boils in $40$ minutes. If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be ...... $min$
AIPMT 2003, Medium
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$Q=\frac{V^2}{R_1} \times t_1=\frac{V^2}{R_2} \times t_2=\frac{V^2}{R} \times t$
$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R^2} \Rightarrow \frac{Q}{V^2 t}=\frac{Q}{V^2 t_1}+\frac{Q}{V^2 t_2}$
$\Rightarrow \frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2} \Rightarrow t=\frac{t_1 t_2}{t_1+t_2}=\frac{10 \times 40}{10+40}$
$=8\; min$
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