The unit of electric permittivity is

$A$ conductor is connected to a battery of $5\, V$. It acquires a charge of $50\ \mu C$. Calculate the capacitance of the conductor in $\mu F$.

$A$ 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).

Eight drops of mercury, each of the same radius and having the same charge, coalesce to form a single larger drop. The capacitance of the larger drop compared to each individual smaller drop is how many times greater?

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of the bigger drop compared to each individual small drop is ........ $\times$.

Two concentric spherical shells $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air. Shell $B$ is given a charge $+Q$ and shell $A$ is grounded. What is the capacitance of the system?