A parallel plate capacitor is to be designed with a voltage rating $1\; k\,V ,$ using a material of dielectric constant $3$ and dielectric strength about $10^{7}\; V\,m ^{-1} .$ (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionisation.) For safety, we should like the field never to exceed, say $10 \%$ of the dielectric strength. What minimum area (in $cm^2$) of the plates is required to have a capacitance of $50\; pF ?$

A parallel plate condenser has a capacitance $50\,\mu F$ in air and $110\,\mu F$ when immersed in an oil. The dielectric constant $'k'$ of the oil is

A capacitor is charged by using a battery which is then disconnected. A dielectric slab is then slipped between the plates, which results in

A parallel plate capacitor is filled with $3$ dielectric materials of same thickness, as shown in the sketch. The dielectric constants are such that $k_3 > k_2 > k_1$. Let the magnitudes of the electric field in and potential drops across each dielectric be $E_3$, $E_2$,$ E_1$, $\Delta V_3$, $\Delta V_2$ and $\Delta V_1$, respectively. Which one of the following statement is true ?

A parallel plate capacitor has two layers of dielectrics as shown in fig. This capacitor is connected across a battery, then the ratio of potential difference across the dielectric layers is