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

[veerubiji]

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.

 

[sandipm14]

Dear Please look at this pdf attached file...

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

 

[dick_freebird]

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

 

[veerubiji]

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

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.

 

[dick_freebird]

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).