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CHAPTER XI.

ALTERNATING CURRENTS.

WE can prove by the doctrine of the conservation of energy that the direction of the induced current in a coil neighbouring to that carrying the inducing current will be opposed in direction to this latter current. For, suppose that the current in the coil on the circuit A B (Fig. 14) induces a current in the coil on the circuit C D in the same direction as itself, as shown by the arrow; on connecting the circuit A B with the circuit CD, as indicated by the dotted line,

we should be able to increase the current flowing through both coils by placing them parallel to each other, for we should have the induced current superimposed on the in

FIG. 14.

ducing current, and in the same direction. We should get an increase of energy merely by placing coils parallel to each other without doing any work. That is, we could get more out of a battery which is supplying the current by placing the coils in the circuit near each other, than we could by placing them apart.

The doctrine of the conservation of energy can also be applied to the determination of the direction of the currents which are produced by moving a coil in a

magnetic field. Let us take the case of the movement of a coil across the face of the pole of a magnet. When we draw the coil away from the pole a current is induced in the coil. This current is due to the change of the flow of induction through the coil; or, as we ordinarily say, it is due to the removal of lines of force from the coil. Now the induced current must flow in such a direction that the attraction of the pole formed by it—the coil becoming for a moment an electro-magnet-on the pole of the magnet must tend to resist the movement of the coil; for if the pole of the electro-magnet repelled the pole of the magnet, we should be assisted in moving the coil away from the magnet, and this would be contrary to the conservation of energy, for we should be gaining more work than we are doing. Let us now see what would happen if, instead of moving a coil from a magnet, we should move the magnet away from the coil. In this case, also, we see that the current induced in the coil must be in such a direction as to resist the movement of the magnet, and if the coil were properly suspended it would follow the magnet. A simple way of trying the experiment is as follows: Suspend a copper disk by a single thread over a magnet which can be made to revolve close to it and under the disk. As the poles of the magnet sweep under the disk currents of electricity are induced in the disk, just as if the disk was made up of coils of wire. These currents flow in such a direction as to oppose the movement of the magnet. They form little electro-magnets, the poles of which attract the poles of the moving magnet, and consequently the disk is swept round with the magnet. In this simple apparatus we have made our first acquaintance with the rotary magnetic field, which is

becoming of such importance in the problem of transmitting power over great distances. The copper disk is the armature of our motor, but we shall see later that it is not necessary to use a rotating magnet. We can produce the same effect by alternating an electric current suitably through electro-magnets which are fixed beneath the disk.

In order to understand the action of fluctuating or alternating currents upon each other, we must consider what is termed the phase of the currents with respect to each other. It is difficult to obtain a clear idea of this word phase, but it is necessary that we should do so.

If, in Fig. 15, a b c d e represents a wave, c being the crest of the wave and d being the trough, and also

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if c and d represent two boats, c will be at the height of its upward movement when d is at the lowest point. The difference of phase of the boats in regard to their relative moment is said to be 180°, for if we draw a circle, ABCM (Fig. 15), we can represent the motion of the boats by the relative movement of two points around the circle. The rise of A to C and the fall of M to the point on the circle opposite C in the same time can be

represented by the curve a b c d e, in which the distances along MY represent the times when A and M have reached different points in their

FIG. 16.

run around the circle. As another illustration, suppose we have two pendulums, one of which, C, Fig. 16, is passing through the middle point of its swing, while the other, D, is returning, having reached the extreme amplitude of its swing. These pendulums have a differ

ence of phase of 90°, and their motions can be represented also by the movements of two bodies around a circle. If the boats c and d were together, they would rise and fall together and would be in the same phase.

As a practical illustration of difference of phase, let us examine the working of the telephone. Is there any difference of phase between the motion of the diaphragm against which we speak and that of the diaphragm to which we listen? The human voice sets the iron diaphragm in motion, and when it is moving swiftest it is causing the greatest disturbance of the lines of induction between it and the magnet of the telephone. The diaphragm of the receiving telephone starts into movement at the instant of this swiftest movement of the sending diaphragm. It is therefore in the condition of a boat at M (Fig. 15) while the sending diaphragm is in the condition of the boat at c. There can be a difference of phase of 90° between them.

Let us now examine what takes place when we put a copper ring in front of an electro-magnet through which

an alternating current is flowing. This alternating or periodic current produces a fluctuation in the flow of induction through the neighbouring copper ring, and an alternating current flows around the ring. If there were no lagging of the current in the ring, due to selfinduction or the setting up of the lines of force in the surrounding medium, the conditions of movement would be represented in Fig. 17, in which the strong line represents the primary or inducing current in the electro-magnet, while the thin line represents the secondary or induced current in the copper ring. The difference of phase between C and D is 90°. Now if the height of the two lines above or below the horizontal line C M represents the strength of the currents at any time, we know that the force between the electro-magnet and the coil is proportional to the product of these currents. If, therefore, we should multiply together the respective distances of two points, such as CD or EF, above and

D

F

M

FIG. 17.

below the middle line C M, we should obtain the force of attraction or repulsion. The strength of the current of induction at C is nothing, and that of the inducing current is CD. Hence, nothing (or zero) multiplied by CD is nothing, and the dotted curve which represents the resultant attraction or repulsion starts from C, and rises and falls in the manner indicated by the dotted

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