HARMONIC ELECTROMOTIVE FORCE AND CURRENT. 53 



length of OP represents the maximum value E (or I) of a 

 harmonic electromotive force (or current), then the vertical pro- 

 jection Ob will represent at each instant the actual value of 

 the harmonic electromotive force e (or current i). 



Consider, for example, the two lines E and I, Fig. 42, which 

 are imagined to be rotating / revolutions per second in the direc- 

 tion of the curved arrow, so that their vertical projections may 

 represent successive instantaneous values of a harmonic electro- 

 motive force and of a har- 

 monic current, respectively. 

 Under these conditions the 

 lines E and I are said to 

 represent the harmonic 

 electromotive force and 

 current, and the diagram, 

 Fig. 42, is called a clock 

 diagram. FIg>42< 



The definitions of cycle, 



period and frequency given in Art. 6 apply also to harmonic 

 electromotive forces and currents. In case of harmonic electro- 

 motive force and current, however, the frequency, f t which is 

 represented by the number of revolutions per second of the lines 

 E and I in Fig. 42, can also be expressed in radians per second, 

 ft> ; and, since there are 2?r radians in a revolution, we have 



*> = 2irf (4) 



22. Phase difference. Consider a harmonic electromotive 

 force e and a harmonic current i of the same frequency. It often 

 happens that the current reaches its maximum value after the 

 electromotive force has passed its maximum value, as shown in 

 Fig. 43. In this case the current is said to lag behind the elec- 

 tromotive force in phase. In some cases the current reaches its 

 maximum value before the electromotive force reaches its maxi- 

 mum value ; and in such a case the current is said to be ahead of 

 the electromotive force in phase. When a current is behind an 



