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.
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