E = 10 r = 1 R = 100 L = 10

Si
1000 +              _..-------------------------------
|           .                        _ _---------
|         .                   .----
|        .                 .-  2 IN SERIES
|       .               .-
|      -
|     .:            - : 
|     .:          .   : 
500 |    . :      __-      -:---------------------------
|   .  :  _.- -       :          2 IN PARALLEL
|  .   :.  -         : 
| .  / :  -           : 
| . /  -             : 
|. / - :              : 
|./.   :              : 
|/_____:_____________:____________________________ t
10     20     40     60     80    100    120

FIG. 54.—­CURVES OF RISE OF CURRENTS.

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