On 12/26/96 I was trying to understand the discharge curve of a 1-farad
capacitor. Here I will comment on the charging data which are shown below
(the abbreviated table). The data refer to the same NEC capacitor as before.
Here again the I=f(t) curve is not exponential (not a straight line on the
semi-log paper for all values of I). And the area under the curve shows that
the charge received is larger than Q=C*V=1*5=5 coulombs. As a matter of fact,
the charge flowing IN during the first 500 seconds was 11.4 coulombs while
the charge flowing OUT, during the same period, was 10.5 coulombs. The
difference is not significant. The data seem to indicate that about one half
of the energy delivered is stored in a non-electric (chemical?) form. Another
alternative is to say that C is 2.2 times larger than the nominal value.
And here is another interesting observation. A fully charged capacitor is
disconnected from the circuit and shortened for a couple of seconds. The
voltage between the terminals, during that time, is zero. I remove the
shorting wire and the voltmeter shows some difference of potential. I had
to keep the short in place for several minutes to get rid of the residual
voltage (to collect the data shown above). Does this support the idea of a
large internal serial resistance? No quantitative investigation of this
effect was undertaken. Can somebody confirm these observations with a
different supercap?
My first attempt to make sense of the non-exponentionality of the discharge
curve was to think that C is increasing when the voltage is lowered (the
effective distance between the "plates" becomes smaller). But this idea is
in conflict with the charging data above. If C were larger for small V then
the effective R*C from the charging curve would be larger at the beginning
(when V is small) and smaller at the end (when V is nearly 5 V). But the
data do not confirm this; the shape of the charging curve is about the same
as the shape of the discharging curve. In both cases the magnitudes of the
slopes seem to be correlated with the magnitudes of currents rather than
with the applied voltages (changes in I are less rapid when the magnitudes
of I are smaller). WHAT IS GOING ON?