Now that the pressure from grading is over I decided to collect some data.
I charged C=1 F to 5 volts and discharged it through an ammeter in
series with a resistor of 100 ohms. The current was measured to see if
it decreases exponentially, as it always does for a "non-chemical"
capacitor. I do remember (reading it somewhere) that chemical reactions
take place in electrolytic capacitors during charging and discharging.
Speculations apart, I am puzzled. Please help me to interpret the discharge
data below. (Actually I have many more data points than shown in the table;
they fit nicely between what is presented.)
t (s) 0 60 120 180 240 310 420 500 660 800 1120 1320 2100
I (mA) 40 27 17.5 12.0 8.0 5.0 2.5 1.5 0.8 0.4 0.17 0.12 0.05
Here is what I did.
1. A linear plot of I versus t was used to get the total charge delivered
by the capacitor (charge is the area under the curve). To my great
surprise Q was found to be 12.9 coulombs. This is 2.6 times as much
as Q= V/C = 5 volts / 1 farad = 5 coulombs. WHERE DOES THE EXTRA Q
COME FROM? IS CAPACITOR ACTING AS A BATTERY (CHEMICAL SEPARATIONS)?
2. A semilogarithmic plot of I versus t was not a straight line over
the entire range of current. It was a piece-wise exponential curve.
The value of RC was changing from about 150 seconds at the beginning
to nearly twice as much at the end. The expected nominal RC was 100
ohms times 1 farad = 100 seconds (or 260 seconds if I assume that
the C of my capacitor is 2.6 F, based on 1 above).
Can somebody verify that R*C is indeed changing during the discharge
process? Perhaps the capacitor I have is a fluke. (It was made by NEC
and labeled as 5.5 V and 1 F. Does it matter which end is + and which
is -? Electrolytic capacitors which I used before were always marked
for + and -.)
3. The initial discharge current (40mA) is smaller than what I expected
(5 volts /100 ohms = 50 mA). I am sure of my 100 ohms. Does it mean
that the esr (equivalent serial resistance) of my cap is 20 ohms?
That is much more than about 0.1 ohms we were talking about.
I wish I had a 500 F (or even 10 F) super-capacitor to see if the
"battery-like" effects (such as delivering more charge than expected)
are stronger. Please share your experimental data.