32 ELEMENTS OF ELECTRICAL ENGINEERING. 



the effective value of the current, and it is for this reason primarily 

 that the term " effective " value came into use. 



Example. The successive instantaneous values of an alternat- 

 ing electromotive force at equal intervals during a half-cycle are : 

 o, 30, 60, 80, 90, 95, 90, 80, 60 and 30 volts. Dividing the 

 sum of these voltages by their number, 10, gives 61.5 volts 

 which is the average value of the alternating electromotive force 

 during the half-cycle. Squaring each of these voltages, adding 

 these squares and dividing by their number gives the average 

 value of their squares, namely, 4,702.5 volts 2 , and the square 

 root of this average square is the effective value of the alternat- 

 ing electromotive force, namely, 68.6 volts. 



9. Instantaneous and average power delivered by an alternator. 

 Let e be the value, at a given instant, of the electromotive force 

 of an alternator and i the value at the same instant of the cur- 

 rent delivered by the alternator ; then ei is the power in watts 

 which is delivered by the alternator at the given instant, and the 

 average value of ei is the average power delivered by the alter- 

 nator. 



When the alternator delivers current to a circuit which has 

 resistance only, the average value of ei is equal to the effective 

 value of the alternating electromotive force multiplied by the 

 effective value of the alternating current ; but in general the aver- 

 age power delivered by an alternator (average value of ei) is less 

 than the product of effective voltage and effective current. This 

 matter is discussed in Chapters II and III. 



Examples. The full-line curve in Fig. 30 is the electromotive 

 force curve of an alternator, the dotted curve is the current curve 

 for the case in which the alternator delivers current to a circuit 

 which has resistance only, and the ordinates of the dot-dash 

 curve represent the successive instantaneous values of the power 

 ei delivered by the alternator. In this case the values of ei are 

 all positive but they vary from zero to a certain maximum value. 

 That is to say, the alternator delivers power in pulses, one for 

 each half-cycle of electromotive force and current. 



