The capacitance of a parallel plate capacitor with air as medium is `3muF`. With the introduction of a dielectric medium between the plates, the capacitance becomes `15muF`. What is the permittivity of the medium? `(epsi_(0)=8.85xx10^(-12)C^(2)//Nm^(2))`

Options

A. `5C^(2)N//m^(2)`
B. `15C^(2)N//m^(2)`
C. `0.44xx10^(-10)C^(2)N//m^(2)`
D. `8.854xx10^(-11)C^(2)N//m^(2)`

Answer

C

Explanation

`C_(1)=(epsi_(0)A)/(d)` with air
and `C_(2)=(K epsi_(0)A)/(d)` (with a dielectric)
`therefore (C_(2))/(C_(1))=K " "therefore K=(15)/(3)=5`
but `K=(epsi)/(epsi_(0))`
`therefore e=Kepsi_(0)=5xx8.85xx10^(-12)`
`=44.25xx10^(-12)=0.4425xx10^(-10)`
`therefore epsiunderset(.)overset(.)(=)0.44xx10^(-10)C^(2)//Nm^(2)`