300 THE POLYPHASE CIRCUIT. 



Star and Mesh Connection of an Alternator. (1) Let the 

 three spirals, Fig. 147, represent the three-phase windings of 

 an alternator, and first suppose them to be star connected 

 as shown. Then the voltage between a pair of conductors 

 A 1 A and jB 1 B forming the transmission line is due to the two 

 windings OA, OB. These windings act in exactly the 

 same way as two alternators giving equal voltages and 

 coupled together at such an angle that they differ in 

 phase by ^ period or 120. The resultant voltage due to 

 these alternators might be found as in Experiment I., and 

 would be represented in magnitude and phase by the 

 diagonal of the parallelogram of which the separate 

 electromotive forces are drawn to form the sides. 



Thus the electromotive force due to the two coils B, 

 A would be represented by two lines E l} E. 2 in a 

 similar manner to the currents in Fig. 146. It must, 

 however, be remembered that when thus represented (see 

 Fig. 149) the lines represent the voltages as + or with 

 respect to 0, and for the conditions shown, the instanta- 

 neous values of the voltage of both coils are equal, and +, 

 and would be represented by projections on E K , 

 which lies to the right of O, and is therefore 

 to be taken as positive. Hence the voltages E 

 and E. 2 in A and B will both be directed away 

 from 0, the common point of the windings, or both 

 towards this point, according to the convention adopted 

 regarding the positive and negative direction. The value 

 of this resultant voltage is seen from Fig. 149 to be E K , equal 

 to the maximum value of each of the component voltages. 

 The voltage which we wish to determine is, however, the 

 resultant voltage between the lines A A 1 and B B 1 , Fig. 147. 

 Thus, if directions away from are considered +, a 

 positive electromotive force in B will be the reverse 

 of a positive electromotive force in A as regards the 

 resultant voltage from B to A. We must therefore reverse 

 the sign of one voltage, shown in Fig. 149, in order to 

 obtain the resultant voltage from B to A. The parallelogram 

 consequently assumes the form given in Fig. 150, where 

 the voltage E., is shown with the arrow pointing 

 in the reverse direction. The parallelogram is now 

 E. 2 l E K E l} the diagonal giving the resultant voltage O E K 

 is therefore longer than in the case represented by 

 Fig. 149. The resultant voltage is, in fact, seen to be 



