Find the capacitance of a conducting sphere of radius $10\mathrm{ }\mathrm{cm}$situated in air. How much charge is required to raise it to a potential of $1000$ volt?

 

Assuming the earth to be a spherical conductor of radius $6400\mathrm{ }\mathrm{km}$, calculate its capacitance.

N drops of mercury of equal radii and possessing equal charges to combine to form a big drop. Compare the charge, capacitance and potential of the bigger drop with the corresponding quantities of individual drops.

A capacitor of $20 \mu \mathrm{F}$ is charged to a potential of $10\mathrm{ }\mathrm{kV}$. Find the charge accumulated on each plate of the capacitor.
  

A parallel plate air capacitor consists of two circular plates of diameter 8 cm. At what distance should the plates be held so as to have the same capacitance as that of a sphere of diameter 20 cm?

A capacitor of unknown capacitance is connected across a battery of V  volt. A charge of $120 \mu \mathrm{C}$ is stored in it. When the potential across the capacitor is reduced by $40\mathrm{ }\mathrm{V},$ the charge stored in the capacitor becomes $40\mathrm{ }\mathrm{\mu C}.$ Calculate V  and the unknown capacitance. What would have been charge in the capacitor if the voltage is increased by $40\mathrm{ }\mathrm{V}$.

A parallel-plate capacitor has plates of area $200\mathrm{ }{\mathrm{cm}}^2$ and separation between the plates  $1.0\mathrm{mm}.$  What potential difference will be developed if a charge of $1.0\mathrm{ }\mathrm{nC}$ is given to the capacitor?

A parallel-plate capacitor has plates of area $200\mathrm{ }{\mathrm{cm}}^2$ and separation between the plates $1.0 \mathrm{mm}$  If the plate separation is now increased to $2.0\mathrm{ }\mathrm{mm}$, what will be the new potential difference?

Two metallic conductors have net charges of $+70 pC$ and $-70 pC$, which result in a potential difference of $20 \mathrm{V}$ between them. What is the capacitance of the system?