92 ALTERNATING CURRENTS 



The insulation thickness in the above table is measured from 

 copper to iron, and includes the insulation of the conductors. 



Since with increasing voltage a greater thickness of insulation 

 becomes necessary, either the size of slot must be increased and this 

 will involve an increase in the diameter of the machine or an 

 equivalent increase must be made in the length of core. High- 

 voltage generators are therefore, for a given power and speed, larger 

 and more expensive than low-voltage ones. Nevertheless, the extra 

 cost of a high-voltage generator is much less than that of the step-up 

 transformers ( 50) which would be necessary with a generator of low 

 voltage. 



44. Calculation of Armature e.m.f. Effect of 

 Varying Length of Polar Arc 



The calculation of the e.m.f. of an alternator is a more difficult 

 and more uncertain matter than the calculation of the e.m.f. of a 

 continuous-current dynamo. This arises from the fact that whereas 

 in the latter case the e.m.f. (for a given speed) depends simply 011 the 

 flux per pole and the number of conductors in series with each other 

 between the brushes, in an alternator the r.m.s. value of the e.m.f. 



depends also on the ratio -- , 'v and the number of slots per pole 

 per phase. This will be evident from the following considerations. 



T)0 1 P^fl T*O 



Let the ratio r be i, and let us, for the sake of simplicity, 

 pole-pitch 



suppose that the field is perfectly uniform under the pole-shoe, and 

 ceases abruptly (without the formation of a magnetic " fringe ") imme- 

 diately outside it. It is then evident that the positive half-wave of 

 e.m.f. induced in a single conductor is of the shape shown in Fig. 78 (a), 

 the e.m.f. having a zero value during the first eighth of a period, a 

 constant value, say E, during the next quarter of a period, and then 

 suddenly falling to a zero value, which is maintained during the re- 

 mainder of the half-period. It is easy to show that the r.m.s. value of 



the e.m.f. is ^E. Suppose next that the pole width is reduced to 



half its original value, the total flux remaining unaltered. On the same 

 assumptions as before, the e.m.f. wave now takes the form shown in 



Fig. 78 (6). The r.m.s. value of the e.m.f. is now E instead of ^ E 



v 2 



as in the first case, notwithstanding the fact that the total flux per 

 pole has remained unaltered, and that the arithmetic mean of the 

 e.m.f. in the conductor is the same as before. Thus for a given flux 



