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 capacitanace to remain the same, the distance between the plates is

Options

A. `8 mm`
B. `6 mm`
C. `10 mm`
D. `12 mm`

Answer

C

Explanation

With air as dielectric,
`C_(0) = (in_(0) A)/(d) = (in_(0) A)/(8xx10^(-3)) = (in_(0) A xx 10^(3))/(8)` …(i)
In the new set up let the distance between the plates to `'d' mm`.
Thickness of dielectric `= 4mm`
Thickness fo air layer `= (d' - 4) mm`
New capacity, `C' = (in_(0) A xx 10^(3))/((4)/(2) + ((d' - 4))/(1)) = (in_(0) A xx 10^(3))/((d' - 2))`
As `C' = C :. (in_(0) A xx 10^(3))/((d' - 2)) = (in_(0) A xx 10^(3))/(8)`
`d' -2 = 8`
`d' = 8 + 2 = 10 mm`