Question

The capacitance of a parallel plate capacitor with air as a medium is 3 µ F. With the introduction of a dielectric medium between the plates, the capacitance becomes 15 µ F.
The permittivity of the medium in SI unit is ______.

[ε₀ = 8.85 × 10^-12 SI unit]

Options

• 8.845 × 10^-11

• 0.4425 × 10^-10

• 15

• 5

Answer 1

The capacitance of a parallel plate capacitor with air as a medium is 3 µ F. With the introduction of a dielectric medium between the plates, the capacitance becomes 15 µ F.
The permittivity of the medium in SI unit is 0.4425 × 10^-10.

Explanation:

The capacitance of a parallel plate capacitor with air is

`"C"=(epsilon_0"A")/"d"`   ...(i)

where, ε₀ = permittivity of free space or air.
The capacitance with a dielectric medium between the plates is

`"C"^'=(epsilon_m"A")/"d"`   ...(ii)

where, ε_m = permittivity of the medium.

Here, C' = 15µF, C = 3µF

and ε₀ = 8.85 × 10^-12 SI unit

From Eqs. (i) and (ii), we get

`"C"^'/"C"=(epsilon_m"A")/"d"xx"d"/(epsilon_0"A") = epsilon_m/epsilon_0`

`epsilon_m=(epsilon_0"C"^')/"C"=(8.85xx10^-12xx15xx10^-6)/(3xx10^-6)`

= 44.25 × 10^-12 SI unit

= 0.4425 × 10^-10 SI unit