Theory and calculation of alternating current phenomena . POLAR COOIWIXATES AND POLAU DIAGRAMS 47where 0 = 2x— is the instantaneous value of the ampHtude 0 corresponding to the instantaneous value, i, of the wave. The instantaneous values are cut out on the movable radiusvector by its intersection with the characteristic circle. Thus, for instance, at the amplitude, AO/?i = Bi = 2tt- (Fig. 38), the fo instantaneous value is OB-^ at the amphtude, AOB2 = 62 = <2 . — 2IT—, the instantaneous value is 0B\ and negative, since into opposition to the radius vector, 052. The angle, 6, so represents
Theory and calculation of alternating current phenomena . POLAR COOIWIXATES AND POLAU DIAGRAMS 47where 0 = 2x— is the instantaneous value of the ampHtude 0 corresponding to the instantaneous value, i, of the wave. The instantaneous values are cut out on the movable radiusvector by its intersection with the characteristic circle. Thus, for instance, at the amplitude, AO/?i = Bi = 2tt- (Fig. 38), the fo instantaneous value is OB-^ at the amphtude, AOB2 = 62 = <2 . — 2IT—, the instantaneous value is 0B\ and negative, since into opposition to the radius vector, 052. The angle, 6, so represents the time, and increasing time isrepresented by an increase of angle 6 in counter-clockwise rota-. FiG. 37. tion. That is, the positive direction, or increase of time, ischosen as counter-clockwise rotation, in conformity with generalcustom. The characteristic circle of the alternating sine wave is deter-mined by the length of its diameter—the intensity of the wave;and by the amplitude of the diameter—the phase of the wave. Hence wherever the integral value of the wave is consideredalone, and not the instantaneous values, the characteristic circlemay be omitted altogether, and the wave represented in intensityand in phase by the diameter of the characteristic circle. Thus, in polar coordinates, the alternating wave may be repre-sented in intensity and phase by the length and direction of. avector, OC, Fig. 38, and its analytical expression would then bec = 0C cos (d - do). This leads to a second vector representation of alternating 48 ALTERXATING-CUKRENT PHENOMENA waves, differing from the crank diagram discussed in Chapter may be called the time diagram or polar diagram,
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