ALTERNATING Cl'RRKNT AND VOLTAGE 



19 



11. Vector Addition of Sine Waves. Assume that it is d< 

 to add the two currents of Fig. 15. This may be done by adding 

 the ordinutes of the two curves at each point, as in Fig. 16, and 

 plotting a new curve, 7 3 . This new curve is the sum of the two 

 currents whose maximum values are 17.0 and 11.3 amp. and 

 elective values 12 and 8 amp. respectively, and the maximum 

 value of this resultant, if measured accurately, will be 24.7 amp. 

 This corresponds to an effective value of 17.45 amp. Therefore, 

 nn of two sine-wave alternating currents, having effective 

 values of 12 and 8 amp. respectively and differing in phase by 

 60, is 17.45 amp. 



IK;. If>. Relation of vector addition of vectors to scalar addition of <>nlin:it>s. 



If the rotating vectors, Fig. 16, be added vectorially by com- 

 pleting the parallelogram, a third vector 7, ; results. This vector 

 / 3 will he found to have a length of iM.7 amp., the exact value of 

 the maximum of the resultant current wave as just found. If a 

 wave be plotted u.-ing / ; as the rotating vector, projecting as 

 . it will coincide wit: -blamed by the addition of the 



ordinates for the I'J- and S-amp. W&VG8. The by which 



idius vector / ; leads /, equals the angle 8 by which the 

 current wave /, le:d< the current wave / . 



bhifl problem can be solved without i:oinii through tin- 

 somewhat lengthy process of plotting the u d adding 

 their ordi: ; merely necessary to lay oil' the maximum 

 ! he waves 60 apart and add them vectorially, just as 



