In an $LC$ circuit,the angular frequency at resonance is $\omega$. What will be the new angular frequency when the inductor's inductance is made two times and the capacitor's capacitance is made four times?

The positive feedback is required by an amplifier to act as an oscillator. The feedback here means ...........

In the $LCR$ circuit shown in the figure,the ac driving voltage is $V = V_m \sin \omega t$.
$(a)$ Write down the equation of motion for $q(t)$.
$(b)$ At $t = t_0$,the voltage source is removed and $R$ is short-circuited. Write down the energy stored in each of $L$ and $C$ at this instant.
$(c)$ Describe the subsequent motion of charges.

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycle/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is

The carrier frequency generated by a tank circuit containing $1 \,nF$ capacitor and $10 \, \mu H$ inductor is

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?