A $500\,\mu F$ capacitor is charged at a steady rate of $100\,\mu C/sec$ . The potential difference across the capacitor will be $10\,V$ after an interval of......$sec$

When a lamp is connected in series with capacitor, then

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........$F$

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A:$ Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.

Reason $R:$ Capacitance of metallic spheres depend on the radii of spheres.

In the light of the above statements, choose the correct answer from the options given below.

A cylindrical capacitor has two co-axial cylinders of length $20 \,cm$ and radii $2 r$ and $r$. Inner cylinder is given a charge $10 \,\mu C$ and outer cylinder a charge of $-10 \,\mu C$. The potential difference between the two cylinders will be

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