HARMONIC ELECTROMOTIVE FORCE AND CURRENT. 59 



maximum value of di\dt is equal to to times the maximum value 

 of i y and difdt is po ahead of i in phase. f 



The meaning of this proposition may be made clear by a clock 

 diagram. Thus the vertical projection of the rotating line I, Fig. 

 50, represents the value of i at each instant, and the vertical pro- 

 jection of the line o>I represents the value of dijdt at each instant. 



The truth of this proposition is evident from the following con- 

 siderations : The length of the rotating line 01, Fig. 51, is I, 

 its angular velocity is a>, and the actual velocity of the end / 

 of the line is o>I, as shown by the dotted arrow in Fig. 51. 

 Furthermore, the vertical projection of this velocity is the velocity 



Fig. 52. 



of the point a, the velocity of a is the rate of change of Oa, and 

 Oa is the value of /. 



The truth of the above proposition may also be shown by 

 differentiating the expression for /, namely, 



which gives 



=I sin <ot 



di T 



= col cos o)t 



dt . 



or 



90) 



The relation between a harmonic alternating current i and its 

 rate of change, dijdt, is so important in the discussion of the 



