What distance $\mathrm{d}$Between the two parallel plates, each of area $\mathrm{A} = 0.0314 {\mathrm{m}}^2$, of an air capacitor be kept so that its capacitance is same as of a conducting sphere of radius $\mathrm{a} = 0.5 \mathrm{m}$?

When a $20 \mathrm{V}$ Battery is connected to an air-capacitor, a charge of $30 \mathrm{\mu C}$ Is obtained on the capacitor. When oil is filled between the plates of the capacitor, then a charge of $75 \mathrm{\mu C}$Is obtained. Calculate the dielectric constant of the oil.

A parallel-plate air capacitor has a plate area of$6 \times {10}^{-3}{\mathrm{m}}^2$ and a plate separation of $3 \mathrm{mm}$. A potential difference of $100 \mathrm{V}$ Is established between its plates by a battery. After disconnecting the battery, the space between the plates is filled by a $3 \mathrm{mm}$ thick mica sheet of dielectric constant$\mathrm{K} = 6$. Find the new$\mathrm{PD}$ Between the plates.