In an LC oscillator,if values of inductance a | vedclass

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

Question

(A) The resonant frequency of an $LC$ oscillator circuit is given by $\omega_0 = \frac{1}{\sqrt{LC}}$.Given that the new inductance $L' = 2L$ and the

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(A) The resonant frequency of an $LC$ oscillator circuit is given by $\omega_0 = \frac{1}{\sqrt{LC}}$.Given that the new inductance $L' = 2L$ and the new capacitance $C' = 8C$.The new resonant frequency $\omega$ is given by $\omega = \frac{1}{\sqrt{L'C'}} = \frac{1}{\sqrt{(2L)(8C)}} = \frac{1}{\sqrt{16LC}}$.Simplifying this,we get $\omega = \frac{1}{4\sqrt{LC}}$.Since $\omega_0 = \frac{1}{\sqrt{LC}}$,we can substitute this into the expression for $\omega$ to get $\omega = \frac{\omega_0}{4}$.Comparing this with $\omega = x\omega_0$,we find that $x = \frac{1}{4}$.

In an $LC$ oscillator,if values of inductance and capacitance become twice and eight times,respectively,then the resonant frequency of the oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is:

Similar Questions

If maximum energy is stored in the capacitor at $t = 0$,find the time after which the current in the circuit will be maximum. Given $L = 25 \, mH$ and $C = 10 \, \mu F$.

The natural frequency of an $LC$ circuit is $120 \ kHz$. When the capacitor in the circuit is totally filled with a dielectric material,the natural frequency of the circuit decreases by $20 \ kHz$. The dielectric constant of the material is:

Obtain the differential equation for an $LC$ circuit.

$A$ 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?

$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. Now,this capacitor is connected to an ideal inductor. When $25\%$ of the energy of the capacitor is transferred to the inductor,what will be the potential difference across the capacitor?

Vedclass Test Series

Exam Paper Generator

Online Exam Module