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The natural frequency of an LC-circuit is 125KHz. Then the capacitor C is replaced by another capacitor with a dielectric medium of dielectric constant k. In this case, the frequency decreases by 25kHz. The value of k is

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3.0

1.7

1.56

2.1

answer is C.

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Detailed Solution

Natural frequency of an LC circuit is $f = \frac{1}{2 π \sqrt{LC}}$ =125 kHz

with introduction of dielectric capacitance will become kC, as frequency reduced by 25 kHz. new frequency would be $f' = \frac{1}{2 π \sqrt{L k C}} = 100 k H z$

$\frac{f'}{f} = \sqrt{k}, \Rightarrow \sqrt{k} = \frac{125}{100} = \frac{5}{4} k = \frac{25}{16} = 1.56$

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