Question

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

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

Answer 1

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

Frequency of $LC$ oscillation= $\frac{1}{2\pi \sqrt{LC}}$
or $\frac{f_1}{f_2}={\left(\frac{L_2{C}_2}{L_1{C}_1}\right]}^{1/2}={\left(\frac{2L\times 4C}{L\times C}\right]}^{1/2}={\left(8\right)}^{1/2}$

$\therefore \frac{f_1}{f_2}=2\sqrt{2}\Rightarrow f_2=\frac{f_1}{2\sqrt{2}}or{f}_2=\frac{f}{2\sqrt{2}}(\therefore f_1=f)$