A capacitance transducer consists of two plates of diameter 2 cm each, separated by an air gap of 0.25 mm.
Find the displacement sensitivity.
What will be an ideal response?
The capacitance is directly proportional to the area of plates and inversely proportional to the distance between them.
The constant of proportionality ?, known as the permittivity, is a function of the type of material separating the plates. For a capacitance transducer with insulating material the capacitance between the plates is defined as:
Where,
Dielectric constant of the insulating medium;
permittivity of air or free space (in vacuum) and is known as 
A = overlapping area in plates, 
d = distance between electrodes or plates (m).
This equation establishes a relationship between the plate area and the distance between the plates.
The right plate is fixed and the left plate is movable by the displacement which is to be measured. The capacitance is computed as:
If air is the dielectric medium, then 
The sensitivity factor can be expressed as:
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