20 



ALTElf\ATI\(! ('('KltENTS 



- arc combined. The resulting vector will be the maximum 

 value of the wave obtained by adding the waves of I\ and 7 2 . 



In practice 1 , one generally has to do with effective rather than 

 maximum values. If the effective values of the waves be added 

 in this same manner, their vector sum is the sum of the two 



45 



FIG. 17. Vector addition of currents, using effective values. 



alternating currents in effective amperes. This is illustrated in 

 Fig. 17, where the 12- and 8-amp. vectors are laid off 60 apart, 

 the 12-amp. vector leading. By completing the parallelogram, 

 the resultant current Oc is obtained. This has a value of 17.45 

 amp. Its value is readily found as follows: 



Project ac upon 06, where ac = 8 

 ab = ac cos 60 = 4.00 

 be = ac sin 60 = 7.45 

 Oc = V(12 + 4.QO) 2 + (7.45) 2 = 17.45 amp. Ans. 



-1CO-V- 



160 V 



00 



Eob 



IK;. 18. Vector addition of two equal voltages having 90 phase difference. 



The angle 6 can be readily determined. 



tan = 



= 0.406 



12+4 

 = 25 



Example. Each of two alternator coils Oa and Ob, Fig. 18 (a), is generating 

 an emf. of 160 volts. These voltages differ in phase by 90. Deter- 



