Now let us apply these most important though rather intricate
considerations to the practical problems of the quick working of the
electromagnet. Take the case of an electromagnet forming some part of
the receiving apparatus of a telegraph system in which it is desired
to secure very rapid working. Suppose the two coils that are wound
upon the horseshoe core are connected together in series. The
coefficient of self-induction for these two is four times as great as
that of either separately; coefficients of self-induction being
proportional to the square of the number of turns of wire that
surround a given core. Now if the two coils instead of being put in
series are put in parallel, the coefficient of self-induction will be
reduced to the same value as if there were only one coil, because half
the line current (which is practically unaltered) will go through each
coil. Hence the time constant of the circuit when the coils are in
parallel will be a quarter of that which it is when the coils are in
series; on the other hand, for a given line current, the final
magnetizing power of the two coils in parallel is only half what it
would be with the coil in series. The two lower curves in Fig. 54
illustrate this, from which it is at once plain that the magnetizing
power for very brief currents is greater when the two coils are put in
parallel with one another than when they are joined in series.
Now this circumstance has been known for some time to telegraph
engineers. It has been patented several times over. It has formed the
theme of scientific papers, which have been read both in France and in
England. The explanation generally given of the advantage of uniting
the coils in parallel is, I think, fallacious; namely that the "extra
currents" (i.e., currents due to self-induction) set up in the two
coils are induced in such directions as tend to help one another when
the coils are in series, and to neutralize one another when they are
in parallel. It is a fallacy, because in neither case do they
neutralize one another. Whichever way the current flows to make the
magnetism, it is opposed in the coils while the current is rising,
and helped in the coils while the current is falling, by the so-called
extra currents. If the current is rising in both coils at the same
moment, then, whether the coils are in series or in parallel, the
effect of self-induction is to retard the rise of the current. The
advantage of parallel grouping is simply that it reduces the time
constant.