1 \ ALTERNATING CURRENTS 



si i. twfl t hat Fo is the vector sum of FI and F 2 and not their algebraic 



sum. 



When more than two vectors are added, the resultant of two is 



first found and this resultant is combined with a third vector, 



etc. This is illustrated in Fig. 10, in which three vectors FI, F 2 



and F 3 are added. 



FI and FZ are first combined 

 and the resultant F r is found. 

 F f is then combined with F 3 , 

 giving FO as the sum of all 

 three vectors, FI, F 2 and F 3 , 

 That is, 



Fo = F! + F 2 + F 3 

 FIG. 10. Sum of three vectors. 



F' is an intermediate vector 

 and therefore does not appear in the ultimate result. 



8. Ohm; Volt. If a resistance of one ohm, as measured with 

 direct current, has no inductance and is so designed that alter- 

 nating current in flowing through it does not produce any 

 secondary effects, such as eddy currents or skin effect, it offers 

 a resistance of one ohm to alternating current. 



When an alternating-current ampere flows through such a 

 resistance, the drop across its terminals is equal to one alternating- 

 current volt. Hence, the relation between maximum and effective 

 volts is the same as the relation between maximum and effective 

 amperes. For a sine wave, the maximum voltage is \/2, or 

 1.414, times the effective voltage. 



9. Phase Relations. The current and voltage in the ordinary 

 alternating-current system have the same fundamental frequency 

 under normal operating conditions, although they do not neces- 

 sarily pass through their corresponding zero values at the same 

 instant. Figure 11 (a) shows two sine-wave currents, one having 

 an effective value of 8 and the other of 12 amp. Their respective 

 maximum values are accordingly 8\/2 or 11.3 amp. and 12\/2 or 

 17.0 amp. Both currents pass through zero, increasing posi- 

 tively, at the same instant and are therefore said to be in phase 

 with each other. 



Figure 11 (6) shows two sine-wave currents of 8 and 12 amp. 

 respectively, but not passing through zero at the same instant. 



