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=(epsilon_(0)A)/(d)`
When dielectric plate (medium) of thickness t is introduced between the plates, then capcity becomes
`C.=(epsilon_(0)A)/(d.-t(1-(1)/(K)))`
but as given,
`C.=C`
`therefore (epsilon_(0)A)/(d)=(epsilon_(0)A)/(d.-t(1-(1)/(K)))`