Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be to times of its initial length if the water is to be boiled in 15 minutes.

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Solution

Q.
Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _ to times of its initial length if the water is to be boiled in 15 minutes. [2024]

1 increased, 4/3

2 increased, 3/4

3 decreased, 3/4

4 decreased, 4/3

Ans.
(3)

   $P = \frac{V^{2}}{R}, R = \frac{ρ L}{A} \Rightarrow P = \frac{V^{2} A}{ρ L}$ or $P \propto \frac{1}{L}$

   $P_{1} \times t_{1} = P_{2} \times t_{2}$

   $\frac{P_{1}}{P_{2}} = \frac{t_{2}}{t_{1}} = \frac{L_{2}}{L_{1}} = \frac{15}{20} \Rightarrow L_{2} = \frac{3}{4} L_{1}$

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