$A$ capacitor of capacitance $C = 900 \, pF$ is charged fully by a $100 \, V$ battery as shown in figure $(a)$. Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance $C = 900 \, pF$ as shown in figure $(b)$. The electrostatic energy stored by the system in figure $(b)$ is $\dots \times 10^{-6} \, J$.

Two identical charged spherical drops,each at a potential $V$,coalesce to form a single larger drop. If the capacitance of each small drop is $C$,find the potential of the larger drop.

Identify the correct statements:
$A$. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
$B$. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to the insulation property of the dielectric.
$C$. Increasing the area of the capacitor plate or decreasing the thickness of the dielectric is an alternate method to increase the capacitance.
$D$. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

In the figure,the area of each plate is $A$ and the distance between consecutive plates is $d$. What is the effective capacitance between points $A$ and $B$?

$A$ combination of capacitors is set up as shown in the figure. The magnitude of the electric field,due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4 \mu F$ and $9 \mu F$ capacitors),at a point distance $30 \ m$ from it,would equal ....... $N/C$.

Consider two charged metallic spheres $S_{1}$ and $S_{2}$ of radii $R_{1}$ and $R_{2},$ respectively. The electric fields $E_{1}$ (on $S_{1}$) and $E_{2}$ (on $S_{2}$) on their surfaces are such that $E_{1} / E_{2} = R_{1} / R_{2}.$ Then the ratio $V_{1} / V_{2}$ of the electrostatic potentials on each sphere is: