$A$ transistor-oscillator using a resonant circuit with an inductor $L$ (of negligible resistance) and a capacitor $C$ in series produces oscillations of frequency $f$. If $L$ is doubled and $C$ is changed to $4C$,the frequency will be

$A$ $1 \mu F$ capacitor is charged to $50 \ V$ and is then discharged through a $10 \ mH$ inductor of negligible resistance. The maximum current in the inductor is (in $A$)

$A$ capacitor of capacitance $2 \mu F$ is charged to a potential difference of $12 \, V$. It is then connected across an inductor of inductance $0.6 \, mH$. The current in the circuit when the potential difference across the capacitor is $6 \, V$ is :

In $L-C$ oscillation,the maximum charge on the capacitor is $Q$. If at any instant,the electric energy and magnetic energy associated with the circuit are equal,then the charge on the capacitor at that instant is:

$A$ $1 \, \mu F$ capacitor is charged to $50 \, V$. The charging battery is then disconnected and a $10 \, mH$ coil is connected across the capacitor so that $LC$ oscillations occur. What is the maximum current in the coil (in $, A$)? Assume that the circuit contains no resistance.

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