Hawkins Electrical Guide v. 01 (of 10) / Questions, Answers, & Illustrations, A progressive course of study for engineers, electricians, students and those desiring to acquire a working knowledge of electricity and its applications

by N. Hawkins

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 illustrated 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 spacing of the vertical arrows representing the magnetic lines, is assumed 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 passes 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 passed through by the wire, be rectified and laid down under each other, as lines 0-1, 1-2, etc., the time of passage of the wire between successive magnetic lines will vary as the length, since the speed is uniform. Thus the wire in passing from line 0 to line 1, takes much more time than in passing from 1 to 2, as indicated at the left of the figure by 0-1 and 1-2, and still less in passing 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.

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 passes 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 passes 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.