how to calculate electric relative permitivity factor of fluid or medium.

Hi,
I am confusing in calculating permitivity of the fluid. Permittivity differs from one fluid to another.
Ɛ=ƐrƐ0.
Since it is an electrical property combined with an electrical capacity, it is possible to measure it indirectly in a capacitive sensor. I have used capacitive sensor to measure electric relative permitivity factor of a dielectric medium can be expressed as a ration of capacity, Cx of capacitor, which space between and around the electrodes is completely filled with the medium, to capacity C0 of the same electrodes in vacuum.
Ɛr= Cx/C0.
I know and measured C0 value. I am facing problems with calculating Cx of capacitor, which space between and around the electrodes is completely filled with the medium.
I am using method as described below.
I am applying an A.C signal (125 KHz) to the capacitive sensor which is filled with some fluid, in response I am getting A.C signal with some phase difference. I am able to measure the amplitudes of sensor input, sensor output signals and their phase difference also. I am trying to make equation that will give Cx value from above known values (Vg (input), Vr (output), ᶲ (phase difference)).
Any help appreciated. Please help me.

Dear Please look at this pdf attached file...

Enjoy it...........

Why not just use the amplitude ratio of plates in fluid
over plates in dry air? That there's your Er.

dick_freebird said:

Why not just use the amplitude ratio of plates in fluid
over plates in dry air? That there's your Er.

Click to expand...

The above formula is not working,

I have measured for decane.
vg=1.9v; Vr= 63mv then amplitude ratio is =1900/63=30,158

Then for air
vg=1.9v; Vr= 36mv then ampiltude ration is =1900/36=52.7

then Er= 30.158/52.7 =0,5. or even

for methonal, Er= 33.

when measure using this method.
Vg=1.9; Vr=1.18v so ration is =1.6.

then Er=1.6/52.7=0.03.

i am getting wrong values.

63mV/36mV (decane/air) ought to be relative permittivity
for the decane. I don't know why you are factoring in the
"amplitude ration" a second time.

Decane should read 2.0; 63/36=1.75. So you might want
a look at accuracy (amplitude linearity from input electrode
to output at low end?) but the outcome of the simple form
is roughly right (10%-ish).