$A$ 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

$A$ $60\,\mu F$ capacitor is charged to $100\,V$. This charged capacitor is connected across a $15\,mH$ coil,so that $LC$ oscillations occur. The maximum current in the coil is:

An $LCR$ circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having a damping constant $b$,the correct equivalence would be:

The charge in an $LC$ circuit with negligible resistance oscillates as given by the equation $\frac{d^2q}{dt^2} + 16\pi^2q = 0$. If the charge is maximum equal to $24\,\mu C$ at $t = 0$,find the charge at $t = \frac{1}{12}\,s$ in $\mu C$.

$A$ capacitor of capacitance $C$ has initial charge $Q_0$ and is connected to an inductor of inductance $L$ as shown. At $t=0$,the switch $S$ is closed. Find the current through the inductor when the energy in the capacitor is three times the energy of the inductor.

$A$ capacitor of capacity $20 \mu F$ is charged to a potential of $35 \text{ V}$. The battery is then disconnected. $A$ pure inductor coil of $200 \text{ mH}$ is connected across the capacitor so that $LC$ oscillations are set up. The maximum current in the coil is: (in $\text{ A}$)