An oscillator circuit consists of an inductance of $0.5 \, mH$ and a capacitor of $20 \, \mu F$. The resonant frequency of the circuit is nearly (in $Hz$)

$A$ $2 \mu F$ capacitor is charged to $50 V$ by a battery. The battery is removed after the capacitor is fully charged. At time $t=0$,a $10 mH$ coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is (in $A s^{-1}$)

$LC$-oscillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

The switch is in position $A$ for a long time. At time $t=0$,it is shifted to position $B$. Find the maximum charge that will accumulate on the capacitor.

$A$ capacitor of capacitance $C$ is charged to a potential $V_1$. It is then connected to an ideal inductor of inductance $L$. When the potential across the capacitor drops to $V_2$,what is the current flowing through the inductor?

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 $...........\,mA$.