With the rise in temperature, the dielectric constant $K$ of a liquid

Two identical capacitors $1$ and $2$ are connected in series. The capacitor $2$ contains a dielectric slab of constant $K$ as shown. They are connected to a battery of emf $V_0\ volts$ . The dielectric slab is then removed. Let $Q_1$ and $Q_2$ be the charge stored in the capacitors before removing the slab and $Q'_1$ , and $Q'_2$ be the values after removing the slab. Then 

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be (Given area of plate $=A$ )

An air capacitor is connected to a battery. The effect of filling the space between the plates with a dielectric is to increase

Capacitance of a capacitor made by a thin metal foil is $2\,\mu F$. If the foil is folded with paper of thickness $0.15\,mm$, dielectric constant of paper is $2.5$ and width of paper is $400\,mm$, then length of foil will be.....$m$

The gap between the plates of a parallel plate capacitor of area $A$ and distance between plates $d$, is filled with a dielectric whose permittivity varies linearly from ${ \varepsilon _1}$ at one plate to ${ \varepsilon _2}$ at the other. The capacitance of capacitor is