The frequency of the output signal of an $LC$ oscillator circuit is $F \ Hz$ with a capacitance of $0.1 \ \mu F$. If the value of the capacitor is increased to $0.2 \ \mu F$,then the frequency of the output signal will be

$LC$-oscillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

$A$ condenser of capacity $6 \ \mu F$ is fully charged using a $6 \ V$ battery. The battery is removed and a resistanceless $0.2 \ mH$ inductor is connected across the condenser. The current flowing through the inductor when one-third of the total energy is in the magnetic field of the inductor is.....$A$

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?

$A$ tuned circuit of a transistor oscillator unit has an inductance of $5 mH$ and a capacitance of $5 pF$. The natural frequency of the oscillator is

Initially,the key was placed on $(1)$ until the capacitor got fully charged. Now,the key is placed on $(2)$ at $t = 0$. Find the minimum time when the energy in both the capacitor and the inductor will be the same.