The natural frequency of an $L-C$ circuit is $125 \ kHz$. When the capacitor is totally filled with a dielectric material,the natural frequency decreases by $25 \ kHz$. The dielectric constant of the material is nearly

$A$ charged $30 \mu\text{F}$ capacitor is connected to a $27 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit (in $\text{ rad/s}$)?

In the $LC$ circuit shown below,the current is in the direction shown. At this time :-

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.....$A$

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

If $L$ and $C$ are inductance and capacitance respectively,then the dimensional formula of $(LC)^{-\frac{1}{2}}$ is