A parallel plate capacitor of area $A$, plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constants $k_1,k_2$ and $k_3$ as shown. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by,

 

 

In the figure, a capacitor is filled with dielectrics. The resultant capacitance is

Consider a parallel plate capacitor of $10 \mu \mathrm{F}$ with air filled in the gap between the plates. Now one-half of the space between the plates is filled with a dielectric of dielectric constant $4$ as shown in the figure. The capacity of the capacitor changes to

In the figure, a potential of $+1200 \mathrm{V}$ is given to point $A$ and point $B$ is earthed, what is the potential at the point $P$.

The charge on $4 \mathrm{\mu F}$ capacitor in the given circuit is (in $\mathrm{\mu C}$)

Four identical capacitors are connected as shown in the diagram. When a battery of $6 \mathrm{V}$ is connected between $A$ and $B$, the charge stored is found to be $1.5 \mu \mathrm{C}.$ The value of $C_1$ is

Figure shows five capacitors connected across a $12 \mathrm{V}$ power supply. What is the charge on the $2 \mu \mathrm{F}$ capacitor?

Three plates $A$, $B$ and $C$ are placed close to each other with $+Q$ charge given to the middle plate. The inner surfaces of A and C can be connected to earth through plate $D$ and keys $K_1$ and $K_2.$ The plate $D$ is a dielectric slab with dielectric constant $K$, then the charge that will flow through plate $D$ when $K_1$ is closed and $K_2$ is open is