The plates of a parallel plate capacitor with air as medium are separated by a distance of `8 mm`. A medium of dielectric constant 2 and thickness `4 mm` having the same area is introduced between the plates. For the capacitance to remain the same, the distance between the plates is

Options

A. 8 mm
B. 6 mm
C. 4 mm
D. 10 mm

Answer

D

Explanation

Original capacity, with air
`C=(epsi_(0)A)/(d)`
When dielectric plate (medium) of thickness t is introduced between the plates, then capacity becomes
`C'=(epsi_(0)A)/(d'-t(1-(1)/(K)))`
But as given, C'=C
`therefore(epsi_(0)A)/(d)=(epsi_(0)A)/(d'-t(1-(1)/(K)))`
`or d=d'-1+4/2implies8=d'-2 or d'=10` mm