Two parallel plate air capacitors have their plate areas `100 and 500 cm^(2)` respectively. If they have the same charge and potential and the distance between the plates of the first capacitor of 0.5 mm, what is the distance between the plates of second capacitor ?

Explanation

Here, two parallel plate capaictors have same charge q and same potential V, so they have equal capacitances as
`C = q//V`,
`C_(1) = C_(2)`
`(in_(0) A_(1))/(d_(1)) = (in_(0) A_(2))/(d_(2))`
or `d_(2) = (A_(2))/(A_(1))d_(1)`
Now `A_(1) = 100 cm^(2), A_(2) = 500 cm^(2)`,
`d_(1) = 0.5 mm = 0.5cm`
`:. d_(2) = (500xx0.05)/(100) = 0.25 cm = 2.5 mm`