In an LC circuit,the angular frequency at res | vedclass

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

Question

(B) The resonant angular frequency of an $LC$ circuit is given by the formula $\omega = \frac{1}{\sqrt{LC}}$.Let the initial inductance be $L$ and cap

Vedclass · Accepted Answer

$\frac{\omega}{4 \sqrt{2}}$

Vedclass · Answer

(B) The resonant angular frequency of an $LC$ circuit is given by the formula $\omega = \frac{1}{\sqrt{LC}}$.Let the initial inductance be $L$ and capacitance be $C$. Then,$\omega = \frac{1}{\sqrt{LC}}$.According to the problem,the new inductance $L' = 4L$ and the new capacitance $C' = 8C$.The new resonant angular frequency $\omega'$ is given by $\omega' = \frac{1}{\sqrt{L'C'}} = \frac{1}{\sqrt{(4L)(8C)}} = \frac{1}{\sqrt{32LC}}$.Simplifying this,we get $\omega' = \frac{1}{\sqrt{16 	imes 2 	imes LC}} = \frac{1}{4 \sqrt{2} \sqrt{LC}}$.Since $\omega = \frac{1}{\sqrt{LC}}$,we can substitute this into the equation to get $\omega' = \frac{\omega}{4 \sqrt{2}}$.

In an $LC$ circuit,the angular frequency at resonance is $\omega$. What is the new angular frequency when the inductance is made four times and the capacitance is made eight times its original value?

Similar Questions

The frequency of oscillation of the current in the given circuit is:

The switch is in position $A$ for a long time. At time $t=0$,it is shifted to position $B$. Find the maximum charge that will accumulate on the capacitor.

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is:

$A$ capacitor is fully charged with a battery. Then the battery is removed and a coil is connected with the capacitor in parallel. How does the current vary?

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module