60 ELEMENTS OF ELECTRICAL ENGINEERING. 



relation of voltage and current, that it is worth while to show 

 this relation in every possible way. Thus, the ordinates of the 

 full-line curve in Fig. 52 represent the successive values of an 

 alternating current i, and the steepness of this curve represents 

 the value of dijdt at each instant. To show the relation be- 

 tween i and dijdt still more clearly, a curve may be drawn, the 

 dotted curve in Fig. 52, of which the ordinates at each point 

 represent the steepness of the current curve. This dotted curve 

 has its maximum value where the current curve crosses the axis ; 

 that is the maximum positive value of dijdt occurs one quarter 

 of a cycle (= 90 of angle) before the maximum positive value 

 of i. 



Example. A harmonic alternating current has a frequency of 

 60 cycles per second or 2ir x 60 radians per second (= o>), 

 and its maximum value is 100 amperes. The maximum rate of 

 change of this current occurs at the instant that the current passes 

 through zero, and it is equal to 2?r x 60 x i oo amperes per 

 second, or 37,699 amperes per second. To force this current 

 through a circuit having an inductance of o. I henry, but having 

 no resistance at all, would require a harmonic electromotive force 

 whose maximum value would be o. i X 37,699 volts, or 3769.9 

 volts, and this electromotive force would be 90 ahead of the 

 current in phase. 



25. Average values and effective values of harmonic electromo- 

 tive forces and currents, (a) .Definition of average value. The 

 average value of any varying quantity y during an interval of time 

 from f to t" is by definition equal to Sj/-A/ divided by the 

 duration of the interval, the summation being extended over the 

 whole interval. That is 



Av. y 



/"-, 

 If the successive values of y be represented by the ordinates 



of the curve ab, Fig. 53, then I ydt is equal to the shaded 



Jt f 



