$A$ thin metal plate $P$ is inserted halfway between the plates of a parallel plate capacitor of capacitance $C$ in such a way that it is parallel to the two plates. The capacitance now becomes

In the given circuit,two identical capacitors $C_1$ and $C_2$ are connected to a battery. The space between the plates of $C_1$ is filled with air,while the space between the plates of $C_2$ is filled with a dielectric material of dielectric constant $K$. Then,

$A$ sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

$A$ parallel plate capacitor has a capacitance $C$. The distance between the two plates is halved and the space between the plates is filled with a dielectric medium. If the new capacitance is $3C$,what is the dielectric constant of the medium?

The capacitance of a capacitor becomes $\frac{7}{6}$ times the original value if a dielectric slab of thickness $t = \frac{2d}{3}$ is introduced between the plates, where $d$ is the distance of separation between the plates. The dielectric constant of the slab is

$A$ parallel plate capacitor is filled with $3$ dielectric materials of the 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 $E_3, E_2, E_1$ and $\Delta V_3, \Delta V_2, \Delta V_1$,respectively. Which one of the following statements is true?