conditions somewhat like fig. 12, and the E.M.F. begins to
rise. In one minute it has gone up by about 0.08 volt, &c.
Fig. 12.
Charge and Discharge.---The most important practical
questions concerning an accumulator are:--its maximum rate
of working; its capacity at various discharge rates; its
efficiency; and its length of life. Apart from mechanical
injury all these depend primarily on the way the cell is
made, and then on the method of charging and discharging.
For each type and size of cell there is a normal maximum
discharging current. Up to this limit any current may
be taken; beyond it, the cell may suffer if discharge be
continued for any appreciable time. The most important
point to attend to is the voltage at which discharge shall
cease. The potential difference at terminals must not fall
below 1.80 volt during discharge at ordinary rates (10
hours) or 1.75 to 1.70 volt for 1 or 2 hour rate. The reason
underlying the figures is simple. These voltages indicate
that the acid in the pores is not being renewed fast enough,
and that if the discharge continue the chemical action will
change: sulphate will not be formed in situ for want of
acid. Any such change in action is fatal to reversibility and
therefore to life and constancy in capacity. To illustrate:
when at slow discharge rates the voltage is 1.80 volt, the
acid in the pores has weakened to a mean value of about
2.5% (see fig. 11), which is quite consistent with some part
of the interior being practically pure water. With high
discharge rates, something like 0.1 volt may be lost in the
cells, by ordinary ohmic fall, so that a voltage reading of
1.73 means an E.M.F. of a little over 1.8 volt, and a very
weak density of the acid inside the pores. Guided by these
figures, an engineer can determine what ought to be the
permissible drop in terminal volts for any given working
conditions. Messrs W. E. Ayrton, C. G. Lamb, E. W. Smith
and M. W. Woods were the first to trace the working of a cell
through varied conditions (Journ. Inst. Elec. Eng., 1890),
and a brief resume of their results is given below.
They began by charging and discharging
between the limits of 2.4 and 1.6 volts.
Fig. 13 shows a typical discharge curve. Noteworthy points are:--(1)
At the beginning and at the end there is a rapid fall in P.D.,
with an intermediate period of fairly uniform value. (2) When the
Fig. 13.
P.D. reaches 1.6 volt the fall is so rapid that there is
no advantage in continuing the action. When the P.D. had
fallen to 1.6 volt the cell was automatically switched into
a charging circuit, and with a current of 9 amperes yielded
the curve in fig. 14. Here again there is a rapid variation in
P.D. (in these cases a rise) at the beginning and end of the
operation. The cells were now carried through the same cycle
several times, giving almost identical values for each cycle.
After some days, however, they became more and more difficult
to charge, and the return on discharge was proportionately
less. It became impossible to charge up to a P.D. of 2.4
volts, and finally the capacity fell away to half its first
value. Examination showed that the plates were badly scaled,
and that some of the scales had partially connected the
plates. These scales were cleared away and the experiments
resumed, limiting the fall of P.D. to 1.8 volt. The
Fig. 14.
difficulties then disappeared, showing that discharge to 1.6
volt caused injury that did not arise at a limit of 1.8. Before
describing the new results it will be useful to examine these
two cases in the light of the theory of E.M.F. already given.
(a) Fall in E.M.F. at beginning of discharge.--At the
moment when previous charging ceases the pores of the positive
plate contain strong acid, brought there by the charging
current. There is consequently a high E.M.F. But the strong
acid begins to diffuse away at once and the E.M.F. falls
rapidly. Even if the cell were not discharged this fall would
occur, and if it were allowed to rest for thirty minutes or
so the discharge would have begun with the dotted line (fig.
13). (b) Final rapid fall.---The pores being clogged by
sulphate the plugs cannot get acid by diffusion, and when
5% is reached the fall in E.M.F. is disproportionately
large (see fig. 10). If discharge be stopped, there is an
almost instantaneous diffusion inwards and a rapid rise
in E.M.F. (c) The rise in E.M.F. at beginning and
end of the charging is due to acid in the pores being
strengthened, partly by diffusion, partly by formation of
sulphuric acid from sulphate, and partly by electrolytic
carrying of strong acid to the positive plate. The injurious
results at 1.6 volt arise because then the pores contain
water. The chemical reaction is altered, oxide or hydrate
is formed, which will partially dissolve, to be changed
to sulphate when the sulphuric acid subsequently diffuses
in. But formed in this way it will not appear mixed with
the active masses in the electrolytic paths, but more or
less alone in the pores. In this position it will more or
less block the passage and isolate some of the peroxide.
Further, when forming in the narrow passage its disruptive
action will tend to force off the outer layers. It is evident
that limitation of P.D. to 1.8 volt ought to prevent these
injuries, because it prevents exhaustion of acid in the plugs.
Fig. 15 shows the results obtained by study of successive
periods of rest, the observations being taken between
the limits of 2.4 and 1.8 volts. Curves A and B show
the state and capacity at the beginning. After a 10
days' rest the capacity was smaller, but repeated cycles
Fig. 15.
of work brought it back to C and D. A second rest (10 days),
followed by many cycles, then gave E and F. After a third
rest (16 days) and many cycles, G and H were obtained.
After a fourth rest (16 days) the first discharge gave I and
the first charge J. Repeated cycles brought the cells back
to K and L. Curves M and N show first cycle after a fifth
rest (16 days); O and P show the final restoration brought
about by repeated cycles of work. The numbers given by the
integration of some of these curves are stated in Table III.
TABLE III.
Capacity and Efficiency under Various
Conditions of Working.
Discharge. Charge. Efficiency.
Experiment. Ampere- Watt Ampere- Watt Quan- Energy.
hours. hours. hours. hours. tity.
--------------------------------------------------------------------
Normal cycle 102 201.7 104.5 230.7 97.2 87.4
Restoration
after 1st rest 100 179 103.8 228.2 96.8 85.8
Restoration
after 2nd rest 91 176.7 103.8 228.2 96.8 85.8
Restoration
after 3rd rest 82.6 161.3 86.2 190.5 95.8 84.7
Discharge
immediately 56.5 110.5 86.2 190.5 65.5 581
after rest . 56.5 110.5 71.1 158.3 79.6 69.6
Restoration
after 8 cycles 80 156.9 83.8 184.6 95.5 85
------------------------------------------------------------------------
The table shows that the efficiency in a normal cycle may be as
high as 87.4%; that during a rest of sixteen days the charged
1 This discharge is here compared with the charge that
preceded the rest; in the next line the same discharge
is compared with the charge following the rest.
accumulator is so affected that about 30% of its charge is
not available, and in subsequent cycles it shows a diminished
capacity and efficiency; and that by repeated charges and
discharges the capacity may be partially restored and the
efficiency more completely so. These changes might be
due to--(a) leakage or short-circuit, (b) some of the
active material having fallen to the bottom of the cell
or (c) some change in the active materials. (a) is
excluded by the fact that the subsequent charge is smaller,
and (b) by the continued increase of capacity during the
cycles that follow the rest. Hence the third hypothesis
is the one which must be relied upon. The change in the
active materials has already been given. The formation of
FIG. 16.
lead sulphate by local action on the peroxide plate and
by diract action of acid on spongy metal on the lead
plate explains the loss of energy shown in curve M, fig.
15, while the fact that it is probably formed, not in
the path of the regular currents, but on the wall of the
grid (remote from the ordinary action), gives a probable
explanation of the subsequent slow recovery. The action of
the acid on the lead during rest must not be overlooked.
We have seen that capacity diminishes as the discharge rate
increases; that is, the available output increases as the
current diminishes. R. E. B. Crompton's diagram illustrating
this fact is given in fig. 16. At the higher rates the
consumption of acid is too rapid, diffusion cannot maintain
its strength in the pores, and the fall comes so much earlier.
The resistance varies with the condition of the cell, as
shown by the curves in fig. 17. It may be unduly increased
by long or narrow lugs, and especially by dirty joints
between the lugs. It is interesting to note that it
increases at the end of both charge and discharge, and
Fig. 17.
much more for the first than the second. Now the composition
of the active materials near the end of charge is almost
exactly the same as at the beginning of discharge, and at
first sight there seems nothing to account for the great
fall in resistance from 0.0115 to 0.004 ohm; that is, to
about one-third the value. There is, however, one difference
between charging and discharging---namely, that due to the
strong acid near the positive, with a corresponding weaker
acid near the negative electrode. The curve of conductivity
for sulphuric acid shows that both strong and weak acid have
much higher resistances than the liquid usually employed in
accumulators, and it is therefore reasonable to suppose that
local variations in strength of acid cause the changes in
resistance. That these are not due to the constitution
of the plugs is shown by the fact that, while the plugs
are almost identical at end of discharge and beginning of
charge, the resistance falls from 0.0055 to 0.0033 ohm.
While a current flows through a cell, heat is produced at
the rate of C2RX0.24 calories (water-gram-degree) per
second. As a consequence the temperature tends to rise.
But the change of temperature actually observed is much
greater during charge, and much less during discharge, than
the foregoing expression would suggest; and it is evident
that, besdies the heat produced according to Joule's law,
there are other actions which warm the cell during charge and
cool it during discharge. Duncan and Wiegand loc. cit.),
who first observed the thermal changes, ascribe the chief
influence to the electrochemical addition of H2SO4 to the
liquid during charge and its removal during discharge. Fig.
18 gives some results obtained by Ayrton, Lamb, &c. This
elevation of temperature (due to electrolytic strengthening
of acid and local action) is a measure of the energy lost
in a cycle, and ought to be minimized as much as possible.
Fig. 18.
Chemistry.---The chemical theory adopted in the foregoing
pages is very simple. It declares that sulphate of
lead is formed on both plates during discharge,
the chemical action being reversed in charging. The
following equations express the experimental results.
Condition before
