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Page 1000 | Volume 4 | Chapter 46 | Alternating Currents

Fig. 1,218. - Application and construction of the sine curve.
Fig. 1,218. (Click to Enlarge)—Application and construction of the sine curve. The sine curve is a wavelike curve used to represent the changes in strength and direction of an alternating current. At the left of the figure is shown an elementary alternator, consisting of a loop of wire ABCD, whose ends are attached to the ring F, and shaft G, being arranged to revolve in a uniform magnetic field, as indicated by the vertical arrows representing magnetic lines at equi-distances. The alternating current induced in the loop is carried to the external circuit through the brushes M and S. The loop, as shown is in its horizontal position at right angles to the magnetic field. The dotted circle indicates the circular path described by AB or CD during the revolution of the loop. Now, as the loop rotates, the induced electric pressure 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 into any number of equal 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) to the perpendiculars; these intersections give points, on the sine curve, for instance, through 2 at the 90° point of the revolution of the loop, and projecting over to the corresponding perpendicular gives 2' 2, whose length is proportional to the electric pressure at that point. In like manner other points are obtained, and the curved line through them will represent the variation in the electric pressure for all points of the revolution. At 90° the pressure 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 pressure, 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.

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