=Ques. What is the object of the field magnet?=

Ans. To provide a magnetic field, through which the conducting loops arranged on a central hub and forming the _armature_ are carried, or the flux carried through them, so that they are successively filled and emptied of magnetic lines.

=Ques. What is a commutator?=

Ans. A device for causing the alternating currents generated in the armature to flow in the same direction in the external circuit.

=Ques. Upon what does the voltage depend?=

Ans. Upon the _rate_ at which each conducting loop is filled and emptied of lines of force and the number of such loops with their grouping or connection.

=Ques. How is the operation of a dynamo best explained?=

Ans. By considering first the action of the simplest form of current generator, or elementary alternator.

=Ques. Describe an elementary alternator.=

Ans. It consists, as shown in fig. 165, of a single rectangular loop of wire A B C D, one end being attached to a ring F and the other to the shaft G, and arranged so as to revolve around the axis X X', which is located midway between the two poles of the magnet. Two metallic strips or _brushes_ M and S connected with the external circuit, bear on the ring F and shaft G, respectively, in order to "collect" the current generated in the armature when the machine is in operation. The long, straight, horizontal arrows joining the two poles of the magnet, represent the _lines of force_ which make up the magnetic field between the poles. The field is here a.s.sumed to be uniform, as indicated by the equal s.p.a.cing of the arrows.

=Ques. What happens when the loop is rotated?=

Ans. According to the law of electromagnetic induction, when the loop is rotated around its horizontal axis in the direction indicated by the curved arrow, an electromotive force will be induced in the loop, the magnitude of which depends on the _rate_ of change of the number of lines of force threading through, or embraced by the loop.

[Ill.u.s.tration: FIG. 165.--Simple elementary alternator. Its parts are a single conducting loop, A B C D, placed between the poles of a permanent magnet, and having its ends connected with a ring, F, and shaft, G, upon which bear brushes M and S, connected with the external circuit. When the loop is rotated clockwise the induced current will flow in the direction indicated by the arrows during the first half of the revolution.]

That is, if the number of lines embraced by the loop be increased from, say, 0 to 1000, or decreased from 1000 to 0, in one second, the electromotive force generated will be two times as great as if the increase or decrease were only 500 lines per second.

=Ques. Upon what does the direction of the induced current depend?=

Ans. Upon the direction of the lines of force and direction of rotation of the loop.

=Ques. How is Fleming's rule applied to determine the direction of current?=

Ans. In applying this rule, the horizontal portion of the loop, such as A B or C D (fig. 165), is to be considered as moving up or down; that is, the component of its motion at right angles to the lines of force is taken as the direction of motion. When the loop is in the position A B C D, such that its plane is vertical or perpendicular to the lines of force, the maximum number of magnetic lines thread through it, but when it is in a horizontal position, A' B' C' D', so that its plane is parallel to the lines of force, no lines pa.s.s through the loop. During the rotation from position A B C D to A' B' C' D', the number of lines pa.s.sing through the loop is _reduced_ from the maximum to zero, the reduction taking place with _increasing rapidity_ as the loop approaches the horizontal position, the electromotive force thus induced _increasing in like proportion_.

Continuing the rotation from the horizontal position A' B' C' D' to the inverted vertical position A B C D (fig. 166), the number of lines pa.s.sing through the loop is increased from zero to the maximum, the increase taking place _with decreasing rapidity_ as the loop approaches the inverted vertical position, the electromotive force thus induced _decreasing in like proportion_.

=Ques. How does the current flow during the first half of the revolution of the loop?=

Ans. It flows in the direction A B C D (fig. 165), as is easily ascertained by aid of Fleming's rule.

[Ill.u.s.tration: FIG. 166.--Simple elementary alternator, showing reversal of current when the loop has made one half revolution from the position of fig. 165. It should be noted that A B, for instance, which has been moving _downward_ during the first half of the revolution (fig. 165), moves _upward_ during the second half (fig. 166); hence, the current during the latter interval flows in the opposite direction.]

=Ques. What is the path of the current to the external circuit?=

Ans. It flows out through brush M (fig. 165) and returns through brush S, thus making M positive and S negative.

=Ques. What occurs during the second half of the revolution?=

Ans. The wire A B (fig. 166), which before was moving in a downward direction, moves in an upward direction; hence, the current is reversed and flows around the loop in the direction A D C B (fig. 166), going out through brush S and returning through brush M. This makes M negative and S positive.

[Ill.u.s.tration: FIG. 167.--Ill.u.s.trating the increase and decrease in the rate magnetic lines are cut by a revolving loop. The initial position of the loop is taken at right angles to the direction of the lines of force.

Since the loop rotates at a constant speed, it is evident that it does not cut the magnetic lines at uniform rate, because the intercepted arcs 0-1, 1-2, etc., are unequal. These arcs, rectified at the right by the horizontal lines 0-1, 1-2, etc., show more clearly the increase and decrease in the rate at which the magnetic lines are cut.]

=Ques. What may be said of the electromotive force during the second half of the revolution?=

Ans. It varies in a similar manner as in the first half of the revolution; that is, the magnetic lines are cut _with increasing rapidity_ during the third quarter, _and with decreasing rapidity_ during the fourth quarter of the revolution, which causes the electromotive force to increase and decrease during these intervals.

The cycle of events just described may be summed up as follows: During the revolution of the loop:

1. From 0 to 90, the electromotive force increases from 0 to maximum; 2. From 90 to 180, the electromotive force decreases from maximum to zero; 3. From 180 to 270, current reverses and the electromotive force increases from zero to maximum; 4. From 270 to 360, the electromotive force decreases from maximum to zero.

It was stated that, during the revolution of the loop, the magnetic lines were cut "with increasing or decreasing rapidity," causing the electromotive force to rise or fall. The reason for this is ill.u.s.trated in fig. 167. The loop is here shown in a horizontal position at right angles to the direction of the magnetic field; the latter, as indicated by the even s.p.a.cing of the vertical arrows representing the magnetic lines, is a.s.sumed to be uniform.

The wire C D of the loop, as it rotates at _constant speed_, cuts the magnetic lines at the points 0, 1, 2, 3, etc., but the distances 0-1, 1-2, 2-3, etc., between these points, are unequal; that is, the wire C D travels farther in cutting the lines 0 and 1, than it does in cutting 1 and 2, and still less in cutting the lines 2 and 3. After cutting the line 4, which pa.s.ses through the axis of revolution, the opposite conditions obtain.

If the arcs 0-1, 1-2, etc., of the dotted circle, which are intercepted by the magnetic lines and pa.s.sed through by the wire, be rectified and laid down under each other, as lines 0-1, 1-2, etc., the time of pa.s.sage of the wire between successive magnetic lines will vary as the length, since the speed is uniform. Thus the wire in pa.s.sing from line 0 to line 1, takes much more time than in pa.s.sing from 1 to 2, as indicated at the left of the figure by 0-1 and 1-2, and still less in pa.s.sing from 2 to 3; that is, the rate of cutting the lines increases as C D rotates from 0 to 4 and decreases from 4 to 8.

Since similar conditions prevail with respect to A B, for its corresponding movement, it is evident that the number of lines which thread through the loop are _decreased with increasing rapidity_ as the loop rotates through the first quarter of a revolution, and _increased with decreasing rapidity_ during the second quarter of the revolution. Moreover, it must be evident that the reverse conditions obtain for the third and fourth quarters of the revolution.

=The Sine Curve.=--In the preceding paragraph it was shown that an alternating current is induced in the armature of either an alternator or dynamo; that is, the current: 1, begins with zero electromotive force, 2, rises to a maximum, 3, decreases again to zero, 4, increases to a maximum in the opposite direction, and 5, decreases to zero.

[Ill.u.s.tration: FIG. 168.--Application and construction of the sine curve.

The sine curve is a wave-like curve used to represent the changes in strength and direction of an alternating current. An elementary alternator is shown at the left to ill.u.s.trate the application of the sine curve to the alternating current cycle. It consists of a loop of wire A B C D, whose ends are attached to the ring F and shaft G, being arranged to revolve in a uniform magnetic field indicated by the vertical arrows which represent magnetic lines at equidistances. The alternating current induced in the loop is carried to the external circuit through the brushes M and S. Now, as the loop rotates, the induced electromotive force will vary in such a manner that its _intensity at any point of the rotation is proportional to the sine of the angle corresponding to that point_, this is represented by the wave-like curve. The mean value of the sine curve, or _average electromotive force_ developed during the revolution, or _period_, is equal to 2 p, or .637 of that of the maximum ordinate, that is, average electromotive force = .637 _amplitude_. The sine curve lies above the horizontal axis during the first half of the revolution and below it during the second half, which indicates that the current flows in one direction for a half revolution and in the opposite direction during the remainder of the revolution.]

A wave-like curve, as shown in fig. 168, is used to represent these several changes, in which the horizontal distances represent time, and the vertical distances, the varying values of the electromotive force. It is called the sine curve because a perpendicular at any point to its axis is proportional to the sine of the angle corresponding to that point.

=Ques. Describe the construction and application of the sine curve.=

Ans. In fig. 168, at the left, is shown an elementary armature in the horizontal position, but at right angles to the magnetic field. The dotted circle indicates the circular path described by A B or C D during the revolution of the loop. Now, as the loop rotates, the induced electromotive force will vary in such a manner that _its intensity at any point of the rotation is proportional to the sine of the angle corresponding to that point_. Hence, on the horizontal line which pa.s.ses through the center of the dotted circle, take any length, as 08, and divide it into any number of parts representing fractions of a revolution, as 0, 90, 180, etc. Erect perpendiculars at these points, and from the corresponding points on the dotted circle project lines parallel to 08; the intersections with the perpendiculars give points on the sine curve.

Thus the loop pa.s.ses through 2 at the 90 point of its revolution, hence, projecting over to the corresponding perpendicular gives 2 2', a point whose elevation from the axis is proportional to the electromotive force at that point. In like manner other points are obtained, and the curved line through them will represent the variation in the electromotive force for all points of the revolution.

At 90, the electromotive force is at a maximum; hence, by using a pressure scale such that the length of the perpendicular 2 2'

for 90 will measure the maximum voltage the length of the perpendicular at any other point will represent the actual pressure at that point.

The curve lies above the horizontal axis during the first half of the revolution, and below it during the second half, which indicates that the current flows in one direction for a half revolution and in the opposite direction during the remainder of the revolution.

The application of the sine curve to represent the alternating cycle, is further ill.u.s.trated in figs. 169 to 173, which show the position of the armature at each quarter of the revolution.

[Ill.u.s.tration: FIGS. 169 to 173.--The sine curve with view of armature for each 90 of the revolution, showing progressively the application of the sine curve to the alternating current cycle.]

In fig. 179, the loop A B C D is in the vertical position at the beginning of the revolution. At this instant the electromotive force is zero, hence the sine curve as shown begins at E, the zero point--that is, on the axis or line of no pressure.

As soon as the loop rotates out of the vertical plane, the electromotive force rises and the current begins to flow in the direction indicated by the arrows, going out to the external circuit through brush M, and returning through brush S.

Continuing the rotation, the electromotive force increases in proportion to the sine of the angle made by the plane of the loop with the horizontal, until the loop comes into the horizontal position ill.u.s.trated in fig. 170. This increase is indicated by the gradual rise of the sine curve from E to F. The loop has now made one quarter of a revolution and the electromotive force reached its maximum value.

As the loop rotates past the horizontal position of fig. 170, the electromotive force gradually decreases in intensity, reaching the zero point at the end of the second quarter--that is, when the loop has turned one half revolution. This is indicated by the gradual fall of the curve from F to G.