$A$ charged $30\; \mu F$ capacitor is connected to a $27\; mH$ inductor. What is the angular frequency of free oscillations of the circuit?

$A$ circuit consists of a coil with inductance $L$ and an uncharged capacitor of capacitance $C$. The coil is in a constant uniform magnetic field such that the flux through the coil is $\phi$. At time $t=0$,the magnetic field is abruptly switched $OFF$. Let $\omega_{0}=1 / \sqrt{L C}$ and ignore the resistance of the circuit. Then,

An ideal capacitor of capacitance $0.2\, \mu F$ is charged to a potential difference of $10\, V$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self-inductance $0.5\, mH$. The current at a time when the potential difference across the capacitor is $5\, V$,is.....$A$

$A$ charged $30\,\mu F$ capacitor is connected to a $27\,mH$ inductor. The angular frequency of free oscillations of the circuit is

An oscillating $LC$ circuit consists of a $75\,mH$ inductor and a $1.2\,\mu F$ capacitor. If the maximum charge on the capacitor is $2.7\,\mu C$,the maximum current in the circuit will be $...........\,mA$.

The square root of the product of inductance $(L)$ and capacitance $(C)$ has the dimension of: