The natural frequency of an LC circuit is 120 | vedclass

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(B) The natural frequency of an $LC$ circuit is given by $f = \frac{1}{2 \pi \sqrt{LC}}$.Given,initial frequency $f = 120 \ kHz$.When a dielectric mat

Vedclass · Accepted Answer

$1.44$

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(B) The natural frequency of an $LC$ circuit is given by $f = \frac{1}{2 \pi \sqrt{LC}}$.Given,initial frequency $f = 120 \ kHz$.When a dielectric material of constant $K$ is introduced,the capacitance becomes $C' = KC$.The new frequency is $f' = f - 20 \ kHz = 120 - 20 = 100 \ kHz$.The new frequency is $f' = \frac{1}{2 \pi \sqrt{L(KC)}} = \frac{1}{\sqrt{K}} 	imes \frac{1}{2 \pi \sqrt{LC}} = \frac{f}{\sqrt{K}}$.Therefore,$\frac{f}{f'} = \sqrt{K}$.Substituting the values: $\frac{120}{100} = \sqrt{K} \Rightarrow 1.2 = \sqrt{K}$.Squaring both sides: $K = (1.2)^2 = 1.44$.

The natural frequency of an $LC$ circuit is $120 \ kHz$. When the capacitor in the circuit is totally filled with a dielectric material,the natural frequency of the circuit decreases by $20 \ kHz$. The dielectric constant of the material is:

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