The frequency of the output signal of an LC o | vedclass

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(A) The frequency of an $LC$ oscillator is given by the formula:$F = \frac{1}{2 \pi \sqrt{LC}}$From this relation,we can see that the frequency $F$ is

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$\frac{F}{\sqrt{2}} \ Hz$

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(A) The frequency of an $LC$ oscillator is given by the formula:$F = \frac{1}{2 \pi \sqrt{LC}}$From this relation,we can see that the frequency $F$ is inversely proportional to the square root of the capacitance $C$ (i.e.,$F \propto \frac{1}{\sqrt{C}}$).Let $F_1 = F$ and $C_1 = 0.1 \ \mu F$.Let $F_2$ be the new frequency and $C_2 = 0.2 \ \mu F$.Using the ratio method:$\frac{F_2}{F_1} = \sqrt{\frac{C_1}{C_2}}$$\frac{F_2}{F} = \sqrt{\frac{0.1}{0.2}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$Therefore,$F_2 = \frac{F}{\sqrt{2}} \ Hz$.

The frequency of the output signal of an $LC$ oscillator circuit is $F \ Hz$ with a capacitance of $0.1 \ \mu F$. If the value of the capacitor is increased to $0.2 \ \mu F$,then the frequency of the output signal will be

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