The following figure shows a $9 \ V$ battery and $3$ uncharged capacitors of capacitances $C_1 = C_2 = C_3 = 1 \ \mu F$. The switch is thrown to the right side until capacitor $C_1$ is fully charged,then the switch is thrown to the left. The final charge on capacitor $C_2$ is (in $\mu C$)

$A$ positive point charge of $10^{-8} \ C$ is kept at a distance of $20 \ cm$ from the center of a neutral conducting sphere of radius $10 \ cm$. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of $10 \ cm$ further away from the center of the sphere along the radial direction. Taking $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ N \cdot m^2 / C^2$ (where $\epsilon_0$ is the permittivity of free space),which of the following statements is/are correct:
$(A)$ Before the grounding,the electrostatic potential of the sphere is $450 \ V$.
$(B)$ Charge flowing from the sphere to the ground because of grounding is $5 \times 10^{-9} \ C$.
$(C)$ After the grounding is removed,the charge on the sphere is $-5 \times 10^{-9} \ C$.
$(D)$ The final electrostatic potential of the sphere is $300 \ V$.

In the circuit shown in the figure, if the point $R$ is earthed and point $P$ is given a potential of $+1800 \, V$, then the charges on $C_2$ and $C_3$ are respectively:

For the circuit shown,which of the following statements is true?

The capacitance of a parallel plate capacitor is $C$ when the region between the plates contains air. This region is now filled with a dielectric slab of dielectric constant $k$. The capacitor is connected to a cell of $emf$ $E$,and the slab is then removed. Which of the following statements is correct?

$A$ capacitor of capacity $C$ is connected to a battery of potential $V$ in parallel. The distance between its plates is reduced to half at once,while the battery remains connected. Then,the energy supplied by the battery to charge the capacitor to potential $V$ again is: