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

$A$ $4 \mu F$ capacitor is charged to $10 \ V$. The battery is then disconnected and a pure $10 \ mH$ coil is connected across the capacitor so that $LC$ oscillations are set up. The maximum current in the coil is (in $A$)

At a moment $t = 0$ when the charge on capacitor $C_1$ is zero,the switch $S$ is closed. If $I_0$ is the current through the inductor at that instant,then for $t > 0,$

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

Compare $LC$ oscillations and forced damped oscillations in mechanics.

$A$ 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