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?

The stratosphere acts as a conducting layer for the earth. If the stratosphere extends beyond $50\mathrm{ }\mathrm{km}$ from the surface of the earth, then calculate the capacitance of the spherical capacitor formed between stratosphere and earth’s surface. Take the radius of the earth as $6400\mathrm{ }\mathrm{km}$.

A charge of $+2.0\times {10}^{-8}\mathrm{ }\mathrm{C}$ is placed on the positive plate and a charge of $-1.0\times {10}^{-8}\mathrm{ }\mathrm{C}$ on the negative plate of a parallel plate capacitor of capacitance $1.2\times {10}^{-3}\mathrm{ }\mathrm{\mu C}$. Calculate the potential difference developed between the plates.
 

Two capacitors of equal capacitance when connected in series have a net capacitance $C_1$, and when connected in parallel have a net capacitance $C_2$. What is the value of ${\mathrm{C}}_1/{\mathrm{C}}_2$?