This definite fraction is the fraction (e - 1)/e; or in decimals,
0.634. All curves of rise of current are alike in general shape, they
differ only in scale, that is to say, they differ only in the height
to which they will ultimately rise, and in the time they will take to
attain this fraction of their final value.
_Example (1)._--Suppose E = 10; R = 200 ohms; L = 8. The final value
of the current will be 0.025 amp. or 25 milliamperes. Then the time
constant will be 8 ÷ 400 = 1-50th sec.
_Example (2)._--The P.O. Standard "A" relay has R = 400 ohms; L =
3.25. It works with 0.5 milliampere current, and therefore will work
with 5 Daniell cells through a line of 9,600 ohms. Under these
circumstances the time constant of the instrument on short circuit is
0.0081 sec.
It will be noted that the time constant of a circuit can be reduced
either by diminishing the self-induction or by increasing the
resistance. In Fig. 54 the position of the time constant for the top
curve is shown by the vertical dotted line at 10 seconds. The current
will take 10 seconds to rise to 0.634 of its final value. This
retardation of the rise of current is simply due to the presence of
coils and electromagnets in the circuit; the current as it grows being
retarded because it has to create magnetic fields in these coils, and
so sets up opposing electromotive forces that prevent it from growing
all at once to its full strength. Many electricians, unacquainted with
Helmholtz's law, have been in the habit of accounting for this by
saying that there is a lag in the iron of the electromagnet cores.
They tell you that an iron core cannot be magnetized suddenly, that it
takes time to acquire its magnetism. They think it is one of the
properties of iron. But we know that the only true time lag in the
magnetization of iron, that which is properly termed "viscous
hysteresis," does not amount to any great percentage of the whole
amount of magnetization, takes comparatively a long time to show
itself, and cannot therefore be the cause of the retardation which we
are considering. There are also electricians who will tell you that
when magnetization is suddenly evoked in an iron bar, there are
induction currents set up in the iron which oppose and delay its
magnetization. That they oppose the magnetization is perfectly true,
but if you carefully laminate the iron so as to eliminate eddy
currents, you will find, strangely enough, that the magnetism rises
still more slowly to its final value. For by laminating the iron you
have virtually increased the self-inductive action, and increased the
time constant of the circuit, so that the currents rise more slowly
than before. The lag is not in the iron, but in the magnetizing
current, and the current being retarded, the magnetization is of
course retarded also.