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

Answer 1

The correct option is B $\frac{f}{2\sqrt{2}}$

We know that for a transitor-oscillator resonant circuit,

$f=\frac{1}{2\pi }\sqrt{\frac{1}{LC}}$

$\Rightarrow \frac{f_1}{f_2}=\sqrt{\frac{L_2{C}_2}{L_1{C}_1}}$

According to problem, $f_1=f,C_1=C,L_1=L$ and
$C_2=4C,L_2=2L$

$\Rightarrow \frac{f}{f2}=\sqrt{\frac{4C\times 2L}{L\times C}}=2\sqrt{2}$

$\therefore f_2=\frac{f}{2\sqrt{2}}$

Hence, $\left(B\right)$ is the correct answer.