One may consider the question of grouping the battery cells from the
same point of view. How does the need for rapid working, and the
question of time constant, affect the best mode of grouping the
battery cells? The amateur's rule, which tells you to so arrange your
battery that its internal resistance should be equal to the external
resistance, gives you a result wholly wrong for rapid working. The
supposed best arrangement will not give you (at the expense even of
economy) the best result that might be got out of the given number of
cells. Let us take an example and calculate it out, and place the
results graphically before our eyes in the form of curves. Suppose the
line and electromagnet have together a resistance of 6 ohms, and that
we have 24 small Daniell cells, each of electromotive force say 1 volt,
and of internal resistance 4 ohms. Also let the coefficient of
self-induction of the electromagnet and circuit be 6 quadrants. When
all the cells are in series, the resistance of the battery will be 96
ohms, the total resistance of the circuit 102 ohms, and the full value
of the current 0.235 ampere. When all the cells are in parallel, the
resistance of the battery will be 0.133 ohm, the total resistance
6.133 ohms, and the full value of the current 0.162 ampere. According
to the amateur rule of grouping cells so that internal resistance
equals external, we must arrange the cells in 4 parallels, each having
6 cells in series, so that the internal resistance of the battery will
be 6 ohms, total resistance of circuit 12 ohms, full value of current
0.5 ampere. Now the corresponding time constants of the circuit in the
three cases (calculated by dividing the coefficient of self-induction
by the total resistance) will be respectively--in series, 0.06 sec.;
in parallel, 0.5 sec.; grouped for maximum steady current, 0.96 sec.
From these data we may now draw the three curves, as in Fig. 55,
wherein the abscissæ are the values of time in seconds and the
ordinates the current. The faint vertical dotted lines mark the time
constants in the three cases. It will be seen that when rapid working
is required the magnetizing current will rise, during short intervals
of time, more rapidly if all the cells are put in series than it will
do if the cells are grouped according to the amateur rule.
|
5| .
| .
| .
4| MAXIMUM .
| OUTPUT \ .
| .
3| .
| . : ALL IN SERIES
| _-------------------:------------------------------
2| .- - :
| - - :
| -: - :
1| / : - : ALL IN PARALLEL
|. : . : _________--------
|- :__ : ----------
+-----------------------------:-------------------------------
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