🚀 go-pugleaf

     The described activity is suitable for for a student project.

According to Gary (PHYGARY@STMARYTX.EDU) the voltmeter input of the MPLI
board from Vernier is seen as a resistor of 3 to 4 gigaohms. Following
his suggestion I tested our Mac-connected version of this apparatus (?).
The DATA LOGGER documentation states that a difference of potential between
0 and +5 volts can be measured using our old ULI box (Universal Laboratory
Inteface). My positive input goes to the center of the RCA jack labeled
"VOLTS INPUT #1", negative to the rim of that jack.

1. A discharged high quality oil capacitor (0.1 microF, 8000 V), already
   connected to ULI, was charged to about 4.5 volts from a power supply.
   Then the power supply was disconnected and volts were measured every
   100 seconds. Here are some representative data (measurement #1 at t=0)

   time (s)      0   100   200   300   400   500   600   700   800
   volts      4.35  3.78  3.37  3.04  2.77  2.54  2.35  2.18  2.03

2. As you can see, volts are changing very slowly indicating that the
   discharging resistance R is about 11 gigaohms. Note that R is due to the
   impedance of the voltmeter R1, in parallel with the leakage resistance of
   the capacitor, R2.  This means that R1>R. Also note that the V-decay
   curve is not exactly exponential; the value of R would be 7.8 gigas on the
   basis of the first three points and 13.7 gigas on the basis of the last
   three points. I will treat 11 gigaohms as the "mean R" over the used
   region of the difference of potential (d.o.p.).

3. How large is R1 if R=11 gigas? The leakage resistance, R2, must be known
   to answer this question. The value of R2 was estimated as follows. First
   the capacitor was fully charged from the power supply of 4.50 volts. It was
   left disconnected for 800 seconds and then connected to the voltmeter. The
   new d.o.p. was found to be 4.05 volts. On the basis of these two readings
   the average value or R2 was found to be 76 gigaohms. This means the mean R1
   is approximately 13 gigaohms.

4. How much of the nonlinearity (dependence of R on the applied voltage) is
   due to the capacitor and how much is due to the voltmeter? This is a good
   topic for a STUDENT RESERACH PROJECT. I do not want to bother you with too
   much data but the nonlinearity becomes more pronounced when the V-decay
   curve is followed for many hours. At 3 volts, for example, the value of R
   is larger than 100 gigaohms. Other factors seem to have an effect on R; I
   do not have time to investigate them. I suspect that a third "gigaresistor"
   R3 (in parallel with R1 and R2) must be present and that its value depends
   of humidity, temerature, pressure, dirt, phase of the moon, and other
   parameters which I did not control.

                    Ludwik Kowalski   kowalski@apollo.montclair.edu