Variable dielectric capacitors

[JohnielWhite]

Good day All:
How can I prove that a linear relationship exist between the displacement (d) and the capacitance(C) of a Variable dielectric capacitor?

I know that the equation for a capacitor's capacitance is:
C= εA/d

[MATLABdude]

I'm not aware of variable dielectric capacitors--are you sure you don't mean a variable capacitor in which the distance between plates is adjusted?

If so, you may have a problem: the capacitance is inversely proportional to the distance between the plates (as per your formula)!

EDIT: Variable capacitor article at Wikipedia:
http://en.wikipedia.org/wiki/Variable_capacitor

[JohnielWhite]

@ MATLABdude Thanks for your response but I read in a book "Industrial Control Handbook" that there are four fundamentals of variable capacitance displacement transducers.
i. Capacitor basics
ii. Variable Seperation
iii.Variable area
iV. Variable Dielectric
From the formula of a parallel plate capacitance:
C=EA/d
It is observed that each term of the formula can be varied to form a displacement transducer.
That is the seperation, area and dielectric. So what I meant by variable dielectric was
when the dielectric moves between the plates causing the permittivity to alter. So from such behavior how can I prove that a linear relationship exist between the capacitance and displacement.

[cmb]

when the dielectric moves between the plates causing the permittivity to alter. So from such behavior how can I prove that a linear relationship exist between the capacitance and displacement.


Can you provide further clarification for you question? You seem to be asking 'how do I prove a distance dependence by changing the dielectric'?

That sounds like it would be similar to asking how you count how many apples you've got, once you know how many bananas you don't? Or how to determine the length of a piece of string by knowing what it is made of.

[jim hardy]

""So what I meant by variable dielectric was
when the dielectric moves between the plates causing the permittivity to alter. ""

i'm trying to think of a real world example. Hewlett Packard used something like that for a level sensor in some surveyor's instruments around 1970.... sorta an electronic version of the bubble you see in a carpenter's level.


anyhow wouldn't you just differentiate the equation for capacitance wrt d ?
if neither area nor epsilon is a f(d) it seems to me you're there...

[JohnielWhite]

Thanks for both your responses...