The frequency of an L-C circuit is f_{1}. If | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The frequency of an ideal $L-C$ circuit is given by $f_{1} = \frac{1}{2\pi\sqrt{LC}}$.When a resistance $R$ is added in series,the circuit becomes

Vedclass · Accepted Answer

$\sqrt{1-\frac{R^{2}C}{4L}}$

Vedclass · Answer

(B) The frequency of an ideal $L-C$ circuit is given by $f_{1} = \frac{1}{2\pi\sqrt{LC}}$.When a resistance $R$ is added in series,the circuit becomes a damped $L-C-R$ circuit. The damped angular frequency is given by $\omega_{d} = \sqrt{\omega_{0}^{2} - \beta^{2}}$,where $\omega_{0} = \frac{1}{\sqrt{LC}}$ and $\beta = \frac{R}{2L}$.Thus,the damped frequency $f_{2}$ is given by:$f_{2} = \frac{1}{2\pi} \sqrt{\left(\frac{1}{\sqrt{LC}}\right)^{2} - \left(\frac{R}{2L}\right)^{2}}$Taking the ratio $\frac{f_{2}}{f_{1}}$:$\frac{f_{2}}{f_{1}} = \frac{\frac{1}{2\pi} \sqrt{\frac{1}{LC} - \frac{R^{2}}{4L^{2}}}}{\frac{1}{2\pi\sqrt{LC}}}$$= \sqrt{\frac{\frac{1}{LC} - \frac{R^{2}}{4L^{2}}}{\frac{1}{LC}}}$$= \sqrt{1 - \frac{R^{2}C}{4L}}$

The frequency of an $L-C$ circuit is $f_{1}$. If a resistance $R$ is also added to it,the frequency becomes $f_{2}$. The ratio $\frac{f_{2}}{f_{1}}$ will be:

Similar Questions

An $L-C$ resonant circuit contains a $400 \ pF$ capacitor and an inductor of $400 \ \mu H$. It is coupled to an antenna. The wavelength of the radiated electromagnetic wave is:

In $L-C$ oscillation,the maximum charge on the capacitor is $Q$. If at any instant,the electric energy and magnetic energy associated with the circuit are equal,then the charge on the capacitor at that instant is:

$A$ resonant $AC$ circuit contains a capacitor of capacitance $10^{-6} \ F$ and an inductor of $10^{-4} \ H$. The frequency of electrical oscillations will be:

In the circuit given below,the capacitor $C$ is charged by closing the switch $S_1$ and opening the switch $S_2$. After charging,the switch $S_1$ is opened and $S_2$ is closed. Find the maximum current in the circuit.

Explain how $LC$ oscillations take place in the circuit.

Vedclass Test Series

Exam Paper Generator

Online Exam Module