. Theory and calculation of alternating current phenomena . ater time. Inversely, a leading current passes the zero line OA earlier,that is, is ahead in the direction of rotation. Instead of the maximum value of the rotating vector, theeffective value is commonly used, especially where the instan-taneous values are not required, but the diagram intended to represent the relations of the dif-ferent alternating waves to eachother. With the length of therotating vector equal to the effect-ive value of the alternating wave,the maximum value obviously is•\/2 times the length of the vector,and the i
. Theory and calculation of alternating current phenomena . ater time. Inversely, a leading current passes the zero line OA earlier,that is, is ahead in the direction of rotation. Instead of the maximum value of the rotating vector, theeffective value is commonly used, especially where the instan-taneous values are not required, but the diagram intended to represent the relations of the dif-ferent alternating waves to eachother. With the length of therotating vector equal to the effect-ive value of the alternating wave,the maximum value obviously is•\/2 times the length of the vector,and the instantaneous values are?\/2 times the projections of thevectors on the horizontal. 18. To combine different sinewaves, their graphical representations as vectors, are combinedby the parallelogram law. If, for instance, two sine waves, OEi, and OE2 (Fig- H), aresuperposed—as, for instance, two acting in the same cir-cuit—their resultant wave is represented by OE, the diagonal of aparallelogram with OEi and OE2 as sides. As the projection of. 22 ALTERNATING-CURRENT PHENOMENA the diagonal of a parallelogram equals the sum of the projectionsof the sides, during the rotation of the parallelogram OE1EE2,the projection of OE on the horizontal OA, that is, the instan-taneous value of the wave represented by vector OE, is equal tothe sum of the projection of the two sides OEi and OE2, that is,the sum of the instantaneous values of the component vectorsOEi and OE2. From the foregoing considerations we have the conclusions:The sine wave is represented graphically in the crank diagram,by a vector, which by its length, OE, denotes the intensity, andby its amplitude, AOE, the phase, of the sine wave. Sine waves are combined or resolved graphically, in vectorrepresentation, by the law of the parallelogram or the polygon ofsine waves. Kirchhofifs laws now assume, for alternating sine waves, theform: (a) The resultant of all the in a closed circuit, as foundby the parallel
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