The frequency of the output signal of an LC oscillator circuit is ' $F$ ' $\mathrm{Hz}$ with a capacitance…
The frequency of the output signal of an LC oscillator circuit is ' $F$ ' $\mathrm{Hz}$ with a capacitance of $0.1 \mu \mathrm{F}$. If the value of the capacitor is increased to $0.2 \mu \mathrm{F}$, then the frequency of the output signal will be
$\frac{F}{\sqrt{2}} \mathrm{~Hz}$
$\frac{F}{\sqrt{3}} \mathrm{~Hz}$
$\frac{F}{2} \mathrm{~Hz}$
$2 F \mathrm{~Hz}$
Solution
The frequency of LC oscillation is given by
$\begin{aligned}
& F=\frac{1}{2 \pi \sqrt{\mathrm{LC}}} \\
& \therefore \frac{F_2}{F_1}=\sqrt{\frac{C_1}{C_2}}=\sqrt{\frac{0.1}{0.2}}=\frac{1}{\sqrt{2}} \\
& \therefore F_2=\frac{F_1}{\sqrt{2}}
\end{aligned}$
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