ROTATING FIELD 33 



In order to find the magnitude of the resultant field, we may 

 determine the sum of all the horizontal components, then the sum of 

 all the vertical components, and finally take the square root of the 

 sum of the squares of the total horizontal and vertical components. 



Now, the total horizontal component at time t is given by 

 (Fig. 23)- 



X = x (u + v) cos 60 = M sin pt + .\M sin pt = M sin pt 

 and the total vertical component by 



Y = (u - v) sin 60 = i}M cos pt 

 so that the magnitude of the resultant field is 



\/XM-~Y a = ijM 



i.e. the resultant field is of constant magnitude. If $ be the angle 

 which it makes with the vertical axis at time t, then 



X 



tan ^ = y = tan pt 



so that the resultant field rotates with constant angular velocity p. 



In this possibility of producing a rotating magnetic field without 

 any mechanical rotation lies, as already mentioned, one of the main 

 advantages of polyphase currents. 



For the production of two-phase currents, two independent sources 

 of e.m.f. are required, having the same frequency but a phase dis- 

 placement of 90. These two sources of e.m.f. are represented by two 

 independent windings in the armature of a two-phase generator. 



Similarly, the three sources of e.m.f. required for the production 

 of three-phase currents are represented by three independent armature 

 windings in the generator. 



16. Connections of Polyphase Systems 



In the case of two-phase systems, the two phases or circuits of 

 the generator, motor, or other receiving apparatus forming the system 

 are, as a rule, kept entirely separate, as there is no advantage in 

 electrically linking them. Sometimes, however, such linkage is 

 resorted to, the arrangement adopted being that shown in Fig. 24. 



If we suppose the system balanced, then the current in the 

 common wire will be represented, in the vector diagram of Fig. 21 (a), 

 by the diagonal of the square constructed on the two current vectors 

 there shown as sides. Hence the current in the common wire is 

 V/2, or 1-414 times the phase current (i.e. the current in either phase), 



D 



