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Q.

An electric kettle has two coils. When one coil is connected to the a.c. mains, water in the kettle boils in 20 minutes. When the other coil is used, the same quantity of water takes 30 minutes to boil. How long will it take for the same quantity of water to boil if the two coils are connected in series ?

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a

25 min

b

30 min

c

35 min

d

50 min

answer is D.

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Detailed Solution

$H = \frac{V^{2}}{R_{1}} t_{1} or R_{1} = \frac{V^{2}}{H} t_{1}$
Further $H = \frac{V^{2}}{R_{2}} t_{2} or R_{2} = \frac{V^{2}}{H} t_{2}$
When resistances are put in series, then
$H = \frac{V^{2}}{R_{s}} t_{s} or R_{s} = \frac{V^{2}}{H} t_{s}$
Now $R_{s} = R_{1} + R_{2}$
$\begin{array}{l} ∴ \frac{V^{2}}{H} t_{s} = \frac{V^{2}}{H} t_{1} + \frac{V^{2}}{H} t_{2} \\ t_{s} = t_{1} + t_{2} \\ = 20 + 30 = 50 \min \end{array}$

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