Alternating Quantities 219 6.14 Addition of Alternating Quantities Consider two alternating currents, i1 Im1 sin t amp and i2 Im2 sin ( t /4) amp, that are to be added together. There are three methods of doing this, as listed below. (a) Plotting them on graph paper. Their ordinates are then added together, and the resultant waveform plotted. This is illustrated in Fig. 6.23 . The amplitude, Im , and the phase angle, f, of the resultant current are then measured from the two axes. i2Imt(rad)i1i0 Fig. 6.23 Thus, sin() ampiItmφNote: Although i i1 i2 , the AMPLITUDE of the resultant is NOT Iml Im2 amp. This would only be the case if i1 and i2 were in phase with each other. (b) Drawing a scaled phasor diagram, as illustrated in Fig. 6.24 . The resultant is found by completing the parallelogram of vectors. The amplitude and phase angle are then measured on the diagram. (c) Resolving the two currents, into horizontal and vertical components, and applying Pythagoras ’ theorem. This method involves using a sketch of the phasor diagram, followed by a purely mathematical process. This phasor diagram, including the identiﬁ cation of the horizontal and vertical components, is shown in Fig. 6.25 . Im1Im2Im/4Scale: 1 cm x amp. Fig. 6.24 /4Im1Im2Im2 cos/4Im2 sin/4 Fig. 6.25