114 ELECTRICAL ENGINEERING 



The power varies with twice the frequency of the current 

 from to EQ!O, but never becomes negative. The area beneath 

 the power curve represents the energy consumed in the circuit 

 during one cycle. 



The average power is 



P = - 



= 1 



7T 



#0/0 L sin 2 01 

 I, _ 



EQ IQ _, f-inr\\ 



E/ ...... 



therefore, the average power in an alternating-current circuit is 

 equal to the product of the effective values of the e.m.f. and the 

 current, if they are in phase. 

 Since 



P = EI 

 and 



E = IR,\ 

 therefore, 



P = I*R, ....... (171) 



and the power is equal to the square of the effective value of the 

 current multiplied by the resistance. 



Case II. If an e.m.f. e = E sin is impressed on a circuit 



containing a resistance R, and an inductive reactance X, the cur- 



X 

 rent will lag behind the e.m.f. by an angle <f> = tan" 1 -~ and its 



instantaneous value will be 



i = 7 sin (0 <). 

 The instantaneous power in the circuit is 



p = d = EQ! Q sin sin (0 0) 



4>)j. . (172) 

 The values of e, i and p for one cycle are plotted in Fig. 82. 



