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# An electric kettle has two coils. When one of these is switched on, the water in the kettle boils in 6 minutes. When the other coil is switched on, the water boils in 3 minutes. If the two coils are connected in parallel , find the time taken to boil the water in the kettle .

$\begin{array}{1 1} 2\;m \\ 10\;m \\ 100\;s \\ 10\;mins \end{array}$

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Solution :
The effective resistance when connected in parallel is
$R^1= \large\frac{R_1R_2}{R_1+R_2}$
$\qquad= \large\frac{2 R_2 \times R_2}{2R_2 +R_2}=\frac{2}{3}$$R_2 \bigg[ \large\frac{R_1}{R_2}$$=2 \;or\; R_1 =2 R_2 \bigg]$
$\large\frac{2/3 R_2}{R_2} =\frac{t^1}{3}$$=2 minutes$