Permittivity of Pyrex/Water

If I understand your description, when you measured with the plates outside the pyrex, between a plate and the other you found pyrex-water-pyrex (neglecting the two thin air gaps between the plates and the pyrex).
You can see this measure as three capacitors in series: one pyrex, one water and a second pyrex. I suspect that you calculated the permittivity ignoring the permittivity and the thickness of the two pyrex capacitors. Am I wrong?

 

Hi,
The inverse of the capacitance of several capacitors in series is the sum of the inverses of capacitances of all capacitors:
(1/Ct) = (1/C1)+ (1/C1)+ ....+ (1/Cn)
Here the three capacitors:
(1/Ct) = (1/Cp) + (1/Cw) + (1/Cp)
For simplicity, let's assume that the capacity of each capacitor can be approximated with the plate capacitor formula. To be valid, dielectric thickness must be much less than dimensions of plates. If the object you have is a cube the approximation is rather coarse, but it helps for the explanation.
Capacity of a plane capacitor is:
C= epsr * epsz * S / th
Here:
epsz = permittivity of vacuum (8.85 10^-12).
epsr = relative permittivity of dielectric (also called dielectric constant).
S = surface of plates.
th = thickness of dielectric.
Now if you write the capacity of all three capacitors and work a little the formulas you will obtain:
Ct= epsz * S / (2 thp / epsrp + thw / epsrw)
Where thp and thw are the thickness of the pyrex and the water.
And epsrp and epsrw are de dielectrics constants of pyrex and water.
The "weird" result is due to the fact that the term thw/epsrw is far smaller than the other: thp/epsrp. Then the total capacity is mainly determined by the pyrex capacitors. From an electrical point of view, the impedance of the water capacitor is almost a short-circuit compared to the impedance of the pyrex capacitors. From an electrostatic point of view, the potential difference is much smaller in the water than in the pyrex.
If instead water you put just air, the situation somewhat inverses and you will mostly see the air. The capacity of the air condenser is less than that of pyrex. But beware, all this depends on the thickness of each dielectric.
Hope that helps.

 

Hi,
First thing, verify your measuring procedure.
Do an approximate estimation of the value of capacitance you are going to measure.
Take a real capacitor with a similar value and measure it with your installation. repeat at other frequencies.
If this works, it will exonerate your multimeter. Then you must examine the geometry of your pyrex capacitor, and also other parasitic capacitances due to the wiring.
Remember that for the formulas to work, "d" must be much smaller than the diameter or any dimension of the plates.
Another possibility is that your multimeter has an internal impedance to low. It must be at least 100 times the value of R. This could cause your negative number under the square root.

I do not understand how you can get U1 > U2. To measure U2 just short-circuit your capacitor with a bit of wire without touching any other part.

Good look.

 

I will not give you any indication that your own teachers wont have given to you.

Tell me: output resistance of your signal generator.
Value of R.
Dimension of your capacitor (approximate).

 

Did you used tap water or distilled o deminaralized water?

 

If you compute de capacitance of your pyrex capacitor, you must find something near 1 nanofarad. the resistance of your capacitor in tap water can be as low as 100 ohms (conductivity of tap water varies from town to town and even from tap to tap). Compute the modulus of the impedance (1/(2 pi F C)) and you will conclude that you must use non conducting water. That is either distilled or demineralized water. You can buy the last in food and hardware stores and even in gas stations (for lead-acid batteries).

Measure U2 short-circuiting the capacitor with a short conductor. Keep yours hands off before reading any measure: your body is resistive and capacitive.

Keep all mains power supply cables as far as possible from the capacitor and multimeter.

Use a high input impedance multimeter. All recent digital multimeters are high impedance.

Test your measuring device with a commercial capacitor, but do not expect to find the nominal value. Real values of most electronic capacitors are within 20% or the nominal value.

Hope that helps.