$A$ $2 \mu F$ 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 $A s^{-1}$)

$A$ 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,

$A$ capacitor of $1\,\mu F$ initially charged to $10\,V$ is connected across an ideal inductor of $0.1\,mH$. The maximum current in the circuit is.....$A$

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.

The frequency of the output signal of an $LC$ oscillator circuit is $F \ Hz$ with a capacitance of $0.1 \ \mu F$. If the value of the capacitor is increased to $0.2 \ \mu F$,then the frequency of the output signal will be

The circuit shown contains an inductor $L$,a capacitor $C$ with an initial charge $CE$,and a battery of $EMF$ $2E$. Find the maximum charge on the capacitor after the switch is closed at $t = 0$.