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. $8 \, f$
• C. $f / 2\sqrt{2}$
• D. $f /2$

Answer 1

Answer: (C)

$f / 2\sqrt{2}$

Answer 2

In a series $LC$ circuit, frequency of $LC$ oscillations is given by $f=\frac{1}{2 \pi \sqrt{L C}}$ or $f \propto \frac{1}{\sqrt{L C}}$ $\Rightarrow \frac{f_{1}}{f_{2}}=\sqrt{\frac{L_{2} C_{2}}{L_{1} C_{1}}}$ Given $L_{1}=L, C_{1}=C, L_{2}=2 L, C_{2}=4 C, f_{1}=f$ $\therefore \frac{f}{f_{2}}=\sqrt{\frac{2 L \times 4 C}{L C}}=\sqrt{8}$ $\Rightarrow f_{2}=\frac{f}{2 \sqrt{2}}$