CHAPTER III. 



HARMONIC ELECTROMOTIVE FORCE AND CURRENT. 



21. Definition of harmonic electromotive force and current. A 



harmonic electromotive force (or current) is an electromotive force 

 (or current) which is at each instant proportional to the sine or 

 cosine of an angle which increases at a constant rate. Thus, wt 

 is an angle which increases at a constant rate, / being elapsed 

 time reckoned from some chosen instant, and a> being a constant, 

 so that a harmonic electromotive force, e, may be represented 

 by the equation : 



e = E sin <>t (3) 



A harmonic electromotive force (or current) is represented, in 

 rectangular coordinates, by a curve of sines of which the abscissas 

 represent elapsed times, and the ordinates represent successive 

 values of electromotive force (or current). 



The clock diagram. A line OP, Fig. 4 1 , rotates at a uni- 

 form angular velocity of f revolutions per second, or o> ( = 27rf) 



Q 



Fig. 41. 



radians per second, about the point O in the direction of the 

 curved arrow, and the vertical projection of OP is at each instant 

 equal to OP times the sine of the angle a>t. Therefore, if the 



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