First slide

L - C Oscillations

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

Moderate

A

f/4
B

8f
C

$f / 2 \sqrt{2}$
D

f/2

Solution

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App