18 



ALTERNA TI.\(! CURRENTS 



frequency of 60 cycles, the radius 7' must make 60 complete 

 revolutions per second, in a counter-clockwise direction. Coun- 

 tei --clockwise rotation has been adopted internationally as the 



ive direction of rotation. 



When the radius /'is at the right-hand horizontal position, the 

 value of the current is zero. When 7' has advanced 30, the point 

 b on the current- wave has been reached. The value of the cur- 

 rent at this instant is ab, or what is the same thing, the current 

 value is given by the distance a'b', the projection of 7' upon the 

 vertical axis. At this particular instant, the distance ab = a'b' = 

 I'/2, since sin 30 = 0.5. 



FIG. 15. Current waves produced by two current vectors differing in phase by 



60. 



Consider two currents, /i and 7 2 , Fig. 15, having effective 

 values of 12.0 and 8.0 amp. respectively. The current 7 2 , whose 

 maximum value is 11.3 amp., lags current /i, whose maximum 

 value is 17.0 amp., by 60. When the radius /i is in the hori- 

 zontal position, the value of 7i is zero at this instant. At this 

 same instant, the radius 7 2 will not have reached its horizontal 

 position, the value of the current being represented by cd, Fig. 15. 

 In fact, the radius 7 2 does not reach its horizontal or zero position 

 until 1 1 has advanced 60 beyond the horizontal. Further, the 

 horizontal distance ce is 60, the same as the phase angle between 

 the two rotating vectors. 



Therefore, these two current-waves can be constructed in their 

 proper phase relation by means of two rotating vectors having 

 lengths of 17.0 and 11.3 amp., having equal angular veloci ties, 

 and differing in phase by 60, Fig. 15. 



