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It takes 16 min to boil some water in an electric kettle. Due to some defect it becomes necessary to remove 10% turns of the heating coil of the kettle. After repairs, how much time will it take to boil the same mass of water?

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17.7 min

14.4 min

20.9 min

13.7 min

answer is B.

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Detailed Solution

If N is the initial number of turns in the coil and r is the radius of coil, then its resistance is

$R = ρ \frac{L}{A} = ρ \frac{N 2 π r}{A} o r \frac{V^{2} t A}{4.2 ρ N 2 π r} = Q = m s d θ$

or $\frac{t}{n} = \frac{m s d θ \times 4.2 ρ 2 π r}{V^{2}} A = c o n s \tan t$

Or $\frac{t_{1} / N_{1}}{t_{2} / N_{2}} = 1 o r t_{2} = \frac{N_{2}}{N_{1}} t_{1} = (\frac{\frac{9}{10} N_{1}}{N_{1}}) t_{1} = \frac{9}{10} \times 16 \min$

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