A transistor-oscillator using a resonant circ | vedclass

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(D) The frequency of an $LC$ oscillator is given by the formula $f = \frac{1}{2\pi\sqrt{LC}}$.Let the initial frequency be $f_1 = f$ with inductance $

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$f / (2\sqrt{2})$

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(D) The frequency of an $LC$ oscillator is given by the formula $f = \frac{1}{2\pi\sqrt{LC}}$.Let the initial frequency be $f_1 = f$ with inductance $L_1 = L$ and capacitance $C_1 = C$.Let the new frequency be $f_2$ with new inductance $L_2 = 2L$ and new capacitance $C_2 = 4C$.Using the ratio of frequencies:$\frac{f_2}{f_1} = \frac{\frac{1}{2\pi\sqrt{L_2 C_2}}}{\frac{1}{2\pi\sqrt{L_1 C_1}}} = \sqrt{\frac{L_1 C_1}{L_2 C_2}}$Substituting the values:$\frac{f_2}{f} = \sqrt{\frac{L 	imes C}{2L 	imes 4C}} = \sqrt{\frac{1}{8}} = \frac{1}{2\sqrt{2}}$Therefore,the new frequency is $f_2 = \frac{f}{2\sqrt{2}}$.

$A$ transistor-oscillator using a resonant circuit with an inductor $L$ (of negligible resistance) and a capacitor $C$ in series produces oscillations of frequency $f$. If $L$ is doubled and $C$ is changed to $4C$,the frequency will be

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