HARMONIC ELECTROMOTIVE FORCE AND CURRENT. 63 



motive force and current, but, since the ratio of maximum values 

 to effective values is a constant according to equations (5) and (6), 

 it is permissible and customary to consider that the lines in a 

 clock diagram represent effective values. 



26. Expression for power in the case of harmonic electromotive 

 force and current. The power developed by an alternating 

 electromotive force pulsates as explained in Art. 9, and the 

 average power (average value of ei) is the important considera- 

 tion. 



The average power P developed by a harmonic electromotive 

 force e (== E sin cot) in maintaining a harmonic current i 

 [=Isin(o>/ 0)] is: 



EI 



or 



(7) 



in which E and / are the effective values of the electromotive 



ECOSB 



Fig. 54. 



Fig. 55. 



force and current respectively, and is their phase difference, as 

 shown in Fig. 54. 



To establish equation (7) it is necessary to find the average 

 value of ei. Using E sin cot for e, and I sm(cot 6) for i, we 

 have : 



ei = EI sin tot sin(cot 0) (a) 



or, since sin(otf 6) = sin cot cos cos cot sin 6, we have : 

 ei = EI cos - sin 2 o>/ EI sin 6 sin cot cos cot 



