ALTERN Arise, CURRENT AND VOLTA( 17 



a sine wave and will have a maximum value of 28.3 amp. corre- 

 sponding to an effective value of 28.3/\/2 = 20 amp. That is, 

 when two currents are in phase their sum is found arithmetically. 

 Figure 16 corresponds to the condition of Fig. 11 (6), whero the 

 unviits differ in phase by 60. Their sum is found in the 

 same manner as in Fig. 13 by adding the two, point by point, 

 and obtaining the resulting current 7 3 . The resultant 7 3 will not 

 have a maximum value of 28.3 amp., as it did when the currents 

 were in phase, but its maximum value will be less, actually 

 being 24.7 amp. This corresponds to an effective value of 17.45 



uitaneous values of current from a rotating vector. 



amp. for the sum of the two, rather than of 20 amp. as before. 

 Therefore, the sum of ani/ number of alternating currents depends 



their [thnxe relnt'umx as well as upon (heir magnitudes. 

 If voltagQfl rather than currents be added, it will be found that 

 th'-ir sum depends upon their phase relations as well as upon their 



10. Vector Representation of Alternating Quantities. It 



was shown in I'ILI. 'J that a sine wave could bo drawn by pro- 

 jectinir a rotating radius, in h ivc positions, to meet cor- 



responding equally-spaced ordinates. The value of t he current 

 or volt a ire may le found at any instant by projecting a radius 

 upon a vertical line. 



Thi- ifl illiM rated in Fiir. 14. A certain current has a maximum 

 value /'. Tin- value /' is laid off a> a radius and this radius 



i in ivvohr mid ccpial to th. 



of tin- current. For example, if the current 7' has a 



2 



