Two circular metal plates each of radius 10 cm are kept parallel to each other at a distance of 1mm. What kind of capacitor do they make ? Mention one application of this capacitor. If the radius of each of the plates is increased by a factor of `sqrt(2)` and thier distance of seperation is decreased to half of its inital value, calculate the ratio of capacitance in the two cases. Suggest a possible method by which the capacitance in second case is increased to n times.

Explanation

These circular metal plates from a parallel plate capacitor. Such a capacitor is used in filter circuits.
`C = (in_(0) A)/(d) = (in_(0) pi r^(2))/(d)` ,
`C' = (in_(0) A')/(d) = (in_(0) pi (sqrt(2) r)^(2))/(d//2) = 4C`
`:. (C )/(C') = (1)/(4)`
In the second case, capacitance will become will become n times by introducing a dielectric of speccific inductive capacity K = n inbetween the plates of the capacitor.