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Three L-C circuits have capacitances in the ratio 1:2:4. All the three capacitors are charged to the same potential and then made to oscillate. If the maximum current in the three circuits are in the ratio of 1:2:6 respectively, then what is the ratio of the inductances of the three circuits ?

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4: 2 : 1

6 : 2 : 1

18 : 9 : 2

18 : 9 : 1

answer is C.

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Detailed Solution

$i_{\max} = V_{0} \sqrt{\frac{C}{L}} \Rightarrow L = \frac{V_{0}^{2} C}{i_{\max}^{2}} L_{1} : L_{2} : L_{3} = \frac{1}{1} : \frac{2}{4} : \frac{4}{36} = 18 : 9 : 2$

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