The capacitance of a parallel-plate capacitor with a uniform dielectric medium between the plates can be calculated using the following formula:
=
⋅
C=
d
ε⋅A
Where:
C is the capacitance of the capacitor.
ε is the permittivity of the dielectric material between the plates.
A is the area of one of the capacitor plates.
d is the distance between the plates.
The permittivity
ε can be further divided into two types: vacuum permittivity (
0
ε
0
) and relative permittivity (
ε
r
) of the dielectric material.
In vacuum,
0
ε
0
is approximately
8.854
×
1
0
−
12
F/m
8.854×10
−12
F/m. The relative permittivity
ε
r
is a dimensionless constant that indicates how much the dielectric material can increase the capacitance compared to a vacuum.
The formula for capacitance with the relative permittivity included is:
=
0
⋅
⋅
C=
d
ε
0
⋅ε
r
⋅A
This formula is valid when the dimensions of the plates are much larger than the distance between them, so the fringe effects at the edges of the plates are negligible.
To summarize, to calculate the capacitance of a parallel-plate capacitor with a uniform dielectric medium:
Determine the vacuum permittivity
0
ε
0
and the relative permittivity
ε
r
of the dielectric material.
Measure or calculate the area
A of one of the capacitor plates.
Measure or determine the distance
d between the plates.
Plug these values into the appropriate formula to calculate the capacitance
C.