In an $LC$ circuit,the capacitor has maximum charge $q_0$. The value of ${\left| {\frac{{di}}{{dt}}} \right|_{\max }}$ is

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

In an oscillation of $L-C$ circuit,the maximum charge on the capacitor is $Q$. The charge on the capacitor,when the energy is stored equally between the electric and magnetic field is

If $C$ and $L$ denote capacitance and inductance respectively,then the dimensions of $LC$ are

In the given circuit, the resonant frequency is (in $ Hz$)

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.