Chapter 5

________________________________________ | | | | | t_{(sec.)} | e^{+(R/L)t} | i_{t} | --------------+--------------+---------| | 0 | 1 | 0 | | 1 | 1.105 | 0.950 | | 2 | 1.221 | 1.810 | | 5 | 1.649 | 3.936 | | 10 | 2.718 | 6.343 | | 20 | 7.389 | 8.646 | | 30 | 20.08 | 9.501 | | 60 | 403.4 | 9.975 | | 120 | 16200.0 | 9.999 | ----------------------------------------

In this case the value of the steady current as calculated by Ohm's law is 10 amperes, but Helmholtz's law shows us that with the great self-induction which we have assumed to be present, the current, even at the end of 30 seconds, has only risen up to within 5 percent. of its final value; and only at the end of two minutes has practically attained full strength. These values are set out in the highest curve in Fig. 54, in which, however, the further supposition is made that the number of spirals, S, in the coils of the electromagnet is 100, so that when the current attains its full value of 10 amperes, the full magnetizing power will be Si = 1000. It will be noticed that the curve rises from zero at first steeply and nearly in a straight line, then bends over, and then becomes nearly straight again, as it gradually rises to its limiting value. The first part of the curve--that relating to the strength of the current after _very small_ interval of time--is the period within which the strength of the current is governed by inertia (i.e., the self-induction) rather than by resistance. In reality the current is not governed either by the self-induction or by the resistance alone, but by the ratio of the two. This ratio is sometimes called the "time constant" of the circuit, for it represents _the time_ which the current takes in that circuit to rise to a definite fraction of its final value.

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 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.

CONNECTING COILS FOR QUICKEST ACTION.

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.

BATTERY GROUPING FOR QUICKEST ACTION.

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 |. : . : _________-------- |- :__ : ---------- +-----------------------------:------------------------------- 0 1 2 3 4 5 6 7 8 9 10

FIG. 55.--CURVES OF RISE OF CURRENT WITH DIFFERENT GROUPINGS OF BATTERY.

When they are all put in series, so that the battery has a much greater resistance than the rest of the circuit, the current rises much more rapidly, because of the smallness of the time constant, although it never attains the same ultimate maximum as when grouped in the other way. That is to say, if there is self-induction as well as resistance in the circuit, the amateur rule does not tell you the best way of arranging the battery. There is another mode of regarding the matter which is helpful. Self-induction, while the current is growing, acts as if there were a sort of spurious addition to the resistance of the circuit; and while the current is dying away it acts of course in the other way, as if there were a subtraction from the resistance. Therefore you ought to arrange the battery so that the internal resistance is equal to the real resistance of the circuit, plus the spurious resistance during that time. But how much is the spurious resistance during that time? It is a resistance proportional to the time that has elapsed since the current was turned on. So then it comes to a question of the length of time for which you want to work it. What fraction of a second do you require your signal to be given in? What is the rate of the vibrator of your electric bell? Suppose you have settled that point, and that the short time during which the current is required to rise is called t; then the apparent resistance at time t after the current is turned on is given by the formula:

R_{t} = R × e^{(R/L)t} + ( e^{(R/L)t} - 1 )

TIME CONSTANTS OF ELECTROMAGNETS.

I may here refer to some determinations made by M. Vaschy,[1] respecting the coefficients of self-induction of the electromagnets of a number of pieces of telegraphic apparatus. Of these I must only quote one result, which is very significant. It relates to the electromagnet of a Morse receiver of the pattern habitually used on the French telegraph lines.

L, in quadrants. Bobbins, separately, without iron cores. 0.233 and 0.265 Bobbins, separately, with iron cores. 1.65 and 1.71 Bobbins, with cores joined by yoke, coils in series 6.37 Bobbins, with armature resting on poles. 10.68

[Footnote 1: "Bulletin de la Societe Internationale des Electriciens," 1886.]

It is interesting to note how the perfecting of the magnetic circuit increases the self-induction.

Thanks to the kindness of Mr. Preece, I have been furnished with some most valuable information about the coefficients of self-induction, and the resistance of the standard pattern of relays, and other instruments which are used in the British postal telegraph service, from which data one is able to say exactly what the time constants of those instruments will be on a given circuit, and how long in their case the current will take to rise to any given fraction of its final value. Here let me refer to a very capital paper by Mr. Preece in an old number of the "Journal of the Society of Telegraph Engineers," a paper "On Shunts," in which he treats this question, not as perfectly as it could now be treated with the fuller knowledge we have in 1890 about the coefficients of self-induction, but in a very useful and practical way. He showed most completely that the more perfect the magnetic circuit is--though of course you are getting more magnetism from your current--the more is that current retarded. Mr. Preece'e mode of experiment was extremely simple. He observed the throw of the galvanometer when the circuit which contained the battery and the electromagnet was opened by a key which at the same moment connected the electromagnet wires to the galvanometer. The throw of the galvanometer was assumed to represent the extra current which flowed out. Fig. 56 represents a few of the results of Mr. Preece's paper.

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FIG. 56.--ELECTROMAGNETS OF RELAY, AND THEIR EFFECTS.

Take from an ordinary relay a coil, with its iron core, half the electromagnet, so to speak, without any yoke or armature. Connect it up as described, and observe the throw given to the galvanometer. The amount of throw obtained from the single coil was taken as unity, and all others were compared with it. If you join up two such coils as they are usually joined, in series, but without any iron yoke across the cores, the throw was 17. Putting the iron yoke across the cores, to constitute a horseshoe form, 496 was the throw; that is to say, the tendency of this electromagnet to retard the current was 496 times as great as that of the simple coil. But when an armature was put over the top, the effect ran up to 2,238. By the mere device of putting the coils in parallel, instead of in series, the 2,238 came down to 502, a little less than the quarter value which would have been expected. Lastly, when the armature and yoke were both of them split in the middle, as is done in fact in all the standard patterns of the British postal telegraph relays, the throw of the galvanometer was brought down from 502 to 26. Relays so constructed will work excessively rapidly. Mr. Preece states that with the old pattern of relay having so much self-induction as to give a galvanometer throw of 1,688, the speed of signaling was only from 50 to 60 words per minute, whereas, with the standard relays constructed on the new plan, the speed of signaling is from 400 to 450 words per minute. It is a very interesting and beautiful result to arrive at from the experimental study of these magnetic circuits.

SHORT CORES _versus_ LONG CORES.

In considering the forms that are best for rapid action, it ought to be mentioned that the effects of hysteresis in retarding changes in the magnetization of iron cores are much more noticeable in the case of nearly closed magnetic circuits than in short pieces. Electromagnets with iron armatures in contact across their poles will retain, after the current has been cut off, a very large part of their magnetism, even if the cores be of the softest of iron. But so soon as the armature is wrenched off, the magnetism disappears. An air gap in a magnetic circuit always tends to hasten demagnetizing. A magnetic circuit composed of a long air path and a short iron path demagnetizes itself much more rapidly than one composed of a short air path and a long iron path. In long pieces of iron the mutual action of the various parts tends to keep in them any magnetization that they may possess; hence they are less readily demagnetized. In short pieces, where these mutual actions are feeble or almost absent, the magnetization is less stable, and disappears almost instantly on the cessation of the magnetizing force. Short bits and small spheres of iron have no magnetic memory. Hence the cause of the commonly received opinion among telegraph engineers that for rapid work electromagnets must have short cores. As we have seen, the only reason for employing long cores is to afford the requisite length for winding the wire which is necessary for carrying the needful circulation of current to force the magnetism across the air gaps. If, for the sake of rapidity of action, length has to be sacrificed, then the coils must be heaped up more thickly on the short cores. The electromagnets in American patterns of telegraphic apparatus usually have shorter cores, and a relatively greater thickness of winding upon them, than those of European patterns.

* * * * *

ELECTRIC ERYGMASCOPE.

The erygmascope is the name of an electric lighting apparatus designed for the examination of the strata of earth traversed by boring apparatus.

It consists of a very powerful incandescent lamp inclosed in a metallic cylinder. One of the two semi-cylindrical sides constitutes the reflector, and the other, which is of thick glass, allows of the passage of the luminous rays, which thus illuminate with great brilliancy the strata of earth traversed by the instrument. The base, which is inclined at an angle of 45°, is an elliptical mirror, and the top, of straight section, is open in order to permit the observer standing at the mouth of the well, and provided with a powerful spyglass, to see in the mirror the image of the earth. The lamp is so mounted that its upwardly emitted rays are intercepted.

The whole apparatus is suspended from a long cable, formed of two conducting wires, which winds around a windlass with metallic journals which are electrically insulated. These journals communicate, through the intermedium of two friction springs, with the conductors on the one hand and, on the other, with the poles of an automatic and portable battery.

This permits of lowering and raising the apparatus at will, without derangement, and without its being necessary to interrupt the light and the observation.--_Revue Industrielle._

* * * * *

A NEW ELECTRIC BALLISTIC TARGET.

The electrical target usually employed in determining velocities of projectiles consists of a wooden frame on which is strung a copper wire so as to make a continuous circuit arranged in parallel vertical lines about one inch or one and one half inches apart.

It frequently happens that a projectile will pass through this target without breaking the circuit, either by squeezing between the wires or because, when last repaired, the target was short-circuited unnoticed, so that the cutting of the wires did not break the circuit. The repair of this target takes considerable time.

_______________________________________________________ | { | +-------------__ --------------__---------------- } | | _ // \\ // \\ } { | | |_| || C_{0} || A || || || A { } | | P \\ // \\ // } { | +------------- --------------- ---------------- } | F { |_______________________________________________________}

Plan. P C =|= _________ |===| ========= A A ========| | S |========\_______/================= |spring | | | | | | | | |S_ | __| |__ __| ||| | | ___________|||______________| |_____________________ | | Section. H / \+/ | | | | | | _____+_____ | | | W | | | |___________|

Besides these objections to this target, another and more serious one is the irregularity in the manner of breaking the circuit. It has been proved that times required for a flat headed and an ogival headed projectile to rupture the current are very different.