Question

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

• A. $f/4$
• B. $8f$
• C. $f/2\sqrt{2}$
• D. $f/2$

Answer 1

Answer: (C)

In a series $LC$ circuit, frequency of $LC$ oscillations is given by
$f=\frac{1}{2\pi \sqrt{LC}}$
or $f\propto \frac{1}{\sqrt{LC}}$
$\Rightarrow \frac{f_1}{f_2}=\sqrt{\frac{L_2{C}_2}{L_1{C}_1}}$
Given
$L_1=L,C_1=C,L_2=2L,C_2=4C,f_1=f$
$\therefore \frac{f}{f_2}=\sqrt{\frac{2L\times 4C}{LC}}=\sqrt{8}$
$\Rightarrow f_2=\frac{f}{2\sqrt{2}}$