If a slab of insulating material (conceptual). $$4 \times 10^{-3} \mathrm{~m}$$ thick is introduced between the plates of a parallel plate capacitor, the separation between the plates has to be increased by $$3.5 \times 10^{-3} \mathrm{~m}$$ to restore the capacity to original value. The dielectric constant of the material will be

Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is

An electrician requires a capacitance of $$6 \mu \mathrm{F}$$ in a circuit across a potential difference of $$1.5 \mathrm{~kV}$$. A large number of $$2 \mu \mathrm{F}$$ capacitors which can withstand a potential difference of not more than $$500 \mathrm{~V}$$ are available. The minimum number of capacitors required for the purpose is

In figure, charge on the capacitor is plotted against potential difference across the capacitor. The capacitance and energy stored in the capacitor are respectively.