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An electric kettle has two coils. When one coil is switched on it takes 15 minutes and the other takes 30 minutes to boil certain mass of water. The ratio of times taken by them, when connected in series and in parallel to boil the same mass of water is :

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1 : 3

5 : 2

7 : 3

9 : 2

answer is D.

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Detailed Solution

Heat delivered by the heater is

$Q = P t \Rightarrow t = \frac{Q}{P}$

Here Power P is

$P = \frac{V^{2}}{R}$

$\Rightarrow t = \frac{Q R}{V^{2}}$

$∴ 15 = \frac{Q R_{1}}{V^{2}} a n d 30 = \frac{Q R_{2}}{V^{2}}$

In series connection :

$t = \frac{Q (R_{1} + R_{2})}{V^{2}} = 45 m i n s$

In parallel connection :

$t = \frac{Q (\frac{R_{1} R_{2}}{R_{1} + R_{2}})}{V^{2}} = \frac{30 \times 15}{45} = 10 m i n s$

Ratio is 9:2

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