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Question

A given quantity of water boils in an electric kettle in $$12 min$$. The length of the heating element in the kettle is $$\iota $$. If the same quantity of water is to boil in $$10 min$$ on the same mains the length of an identical heating element is _______.


A
ι
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B
ι2
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C
3ι4
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D
5ι6
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Solution

The correct option is D $$\displaystyle \frac {5\iota }{6}$$
Amount of heat required to boil a given quantity of water in a constant
$$\displaystyle P=\frac {W}{t}$$ or $$W = H = P \times t = \displaystyle \frac {V^2}{R} \times t = \displaystyle \frac {V^2t_1}{R_1} = \displaystyle \frac {V^2t_2}{R_2}$$
$$\displaystyle \Rightarrow \frac {t_2}{t_1} = \frac {R_2}{R_1} = \frac {l_2}{l_1}$$
or $$\displaystyle \frac {10}{12} = \frac {l_2}{l_1} \Rightarrow l_2 = \frac {10}{12} \times l_1$$
$$\displaystyle l_2 = \frac {5}{6}l$$

Physics

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