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

A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V\ volt$. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

A spherical capacitor has an inner sphere of radius $12 \;cm$ and an outer sphere of radius $13\; cm .$ The outer sphere is earthed and the inner sphere is given a charge of $2.5\; \mu \,C .$ The space between the concentric spheres is filled with a liquid of dielectric constant $32$

$(a)$ Determine the capacitance of the capacitor.

$(b)$ What is the potential of the inner sphere?

$(c)$ Compare the capacitance of this capacitor with that of an isolated sphere of radius $12 \;cm .$ Explain why the latter is much smaller.

The parallel combination of two air filled parallel plate capacitors of capacitance $C$ and $nC$ is connected to a battery of voltage, $V$. When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant $K$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is

In a capacitor of capacitance $20\,\mu \,F$, the distance between the plates is $2\,mm$. If a dielectric slab of width $1\,mm$ and dielectric constant $2$ is inserted between the plates, then the new capacitance is……$\mu \,F$