A parallel plate condenser with oil (dielectric constant 2) between the plates has capacitance C. If oil is removed, the capacitance of capacitor becomes

Options

A. `sqrt(2C)`
B. `2C`
C. `(C)/(sqrt2)`
D. `(C)/(2)`

Answer

D

Explanation

The capacitance of a parallel plate capacitor with dielectric (oil) between its plates is.
`C=(Kepsi_(0)A)/(d).....(i)`
where `epsi_(0)`,=electric permittivity of free space
K=dielectric constant
A=area of each plate of capacitor
d=distance between two plates
When dielectric (oil) is removed, so capacitance `c_(0)=(epsi_(0)A)/(d).....(ii)`
Comparing Eqs. (i) and (iii), we get
`C=KC_(0)`
`Rightarrow C_(0)=(C)/(K)=(C)/(2) (therefore K=2)`