We have three identical metallic spheres $A, B$ and $C$. $A$ is given a charge $Q$, and $B$ and $C$ are uncharged. The following processes of touching of two spheres are carried out in succession. Each process is carried out with sufficient time.
$(i)$ $A$ and $B$      $(ii)$ $B$ and $C$
$(iii)$ $C$ and $A$      $(iv)$ $A$ and $B$
$(v)$ $B$ and $C$
The final charges on the spheres are

In a spherical condenser radius of the outer sphere is $R$. The different in the radii of outer and inner sphere in $x$. Its capacity is proportional to

Consider the situation shown in the figure. The capacitor $A$ has a charge $q$ on it whereas $B$ is uncharged. The charge appearing on the capacitor $B$ a long time after the switch is closed is

$1000$ small water drops each of capacitance $C$ join together to form one large spherical drop. The capacitance of bigger sphere is ......... $C$

A cylindrical capacitor has two co-axial cylinders of length $15\; cm$ and radii $1.5 \;cm$ and $1.4\; cm .$ The outer cylinder is earthed and the inner cylinder is given a charge of $3.5\; \mu \,C .$ Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

A spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed will be