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

A parallel plate capacitor of capacitance $5\,\mu F$ and plate separation $6\, cm$ is connected to a $1\, V$ battery and charged. A dielectric of dielectric constant $4$ and thickness $4\, cm$ is introduced between the plates of the capacitor. The additional charge that flows into the capacitor from the battery is........$\mu C$

Capacitance of a parallel plate capacitor becomes $4/3$ times its original value if a dielectric slab of thickness $t = d/2$ is inserted between the plates ($d$ is the separation between the plates). The dielectric constant of the slab 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.

Write the formula of capacitance of capacitor having dielectric constant $\mathrm{K} = 2$.

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