A transistor-oscillator using a resonant circ | vedclass

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(D) The frequency of an $L-C$ resonant circuit is given by the formula: $f = \frac{1}{2 \pi \sqrt{LC}}$.Let the initial frequency be $f_1 = f$ with in

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

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(D) The frequency of an $L-C$ resonant circuit 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 $C_1 = C$.The new frequency $f_2$ with $L_2 = 2L$ and $C_2 = 4C$ is given by:$f_2 = \frac{1}{2 \pi \sqrt{L_2 C_2}} = \frac{1}{2 \pi \sqrt{(2L)(4C)}}$.Comparing the two frequencies:$\frac{f_2}{f_1} = \frac{\frac{1}{2 \pi \sqrt{8LC}}}{\frac{1}{2 \pi \sqrt{LC}}} = \sqrt{\frac{LC}{8LC}} = \frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}}$.Therefore,$f_2 = \frac{f}{2\sqrt{2}}$.

$A$ 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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