A parallel plate capacitor with air between the plates has a capacitance of \(8~p\text{F}.\). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant \(6?\)
1. \(48~p\text{F}\)
2. \(8~p\text{F}\)
3. \(96~p\text{F}\)
4. \(60~p\text{F}\)

A parallel plate capacitor is to be designed with a voltage rating of \(1 ~\text{kV},\) using a material of dielectric constant \(3\) and dielectric strength of about \(10^7 ~\text{V m}^{-1}.\) For safety, we should like the field never to exceed, say \(10\%\) of the dielectric strength. What minimum area of the plates is required to have a capacitance of \(50~\text{pF}?\)
1. \(19~\text{cm}^2\)
2. \(17~\text{cm}^2\)
3. \(15~\text{cm}^2\)
4. \(23~\text{cm}^2\)