$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $6 \ V$. Another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $2 \ V$. The total energy of both combinations is the same. The value of $C_2$ in terms of $C_1$ is:

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.

$A$ fully charged capacitor has a capacitance $C$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $s$ and mass $m$. If the temperature of the block is raised by $\Delta T$,the potential difference $V$ across the capacitor is

Two capacitors each of $1\,\mu F$ capacitance are connected in parallel and are then charged by a $200\,V$ $d.c.$ supply. The total energy of their charges (in $joules$) is

$A$ soap bubble of radius $R$ and surface tension $T$ is formed in a vacuum. It is slowly charged so that it slowly expands. It stops charging when the radius becomes $2R$. Find the amount of charge given to the bubble.

There exists a uniform electric field $E = 4 \times 10^5 \, Vm^{-1}$ directed along the negative $x$-axis such that the electric potential at the origin is zero. $A$ charge of $-200 \, \mu C$ is placed at the origin,and a charge of $+200 \, \mu C$ is placed at $(3 \, m, 0)$. The electrostatic potential energy of the system is ........... $J$.