Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is

The potentials of the two plates of capacitor are $+10\,V$ and $-10\, V$. The charge on one of the plates is $40 \,C$. The capacitance of the capacitor is........$F$

When we touch the terminals of a high voltage capacitor, even after a high voltage has been cut off, then the capacitor has a tendency to

Two identical charged spherical drops each of capacitance $C$ merge to form a single drop. The resultant capacitance is

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement $1$ : It is not possible to make a sphere of capacity $1$ farad using a conducting material.
Statement $2$ : It is possible for earth as its radius is $6.4\times10^6\, m$

The capacitance $(C)$ for an isolated conducting sphere of radius $(a)$ is given by $4\pi \varepsilon_0a$. If the sphere is enclosed with an earthed concentric sphere. The ratio of the radii of the spheres $\frac{n}{{(n - 1)}}$  being then the  capacitance of such a sphere will be increased by a factor