A parallel plate capacitor having a dielectric constant 5 and dielectric strength $$10^6 \mathrm{~V} \mathrm{~m}^{-1}$$ is to be designed with voltage rating of $$2 \mathrm{~kV}$$. The field should never exceed $$10 \%$$ of its dielectric strength. To have the capacitance of $$60 \mathrm{~pF}$$ the minimum area of the plates should be

The figure shows a network of five capacitors connected to a 20 V battery. Calculate the charge acquired by each 10 $$\mu$$F capacitor.

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as $$\epsilon=2 U$$. A similar capacitor with no dielectric is charged to $$U_0=78 \mathrm{~V}$$. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

A capacitor of capacity $$2 ~\mu \mathrm{F}$$ is charged upto a potential $$14 \mathrm{~V}$$ and then connected in parallel to an uncharged capacitor of capacity $$5 ~\mu \mathrm{F}$$. The final potential difference across each capacitor will be