CHAP. IV] INDUCED E.M.F. 63 



of turns in the primary and secondary windings: that is, we 

 have Ei:E 2 = Ni:N 2 . 



Prob. 7. A 60-cycle transformer is to be designed so as to have a flux 

 density in the core of about 9 kl./sq.cm.; the difference of pot 



en consecutive turns must not exceed 5 volts. What is the required 

 cross-section of the iron? Ans. 210 sq.cm. 



Prob. 8. The transformer in the preceding problem is to be wound for 

 6600 v. primary, and 440 v. secondary. What are the required numbers 

 of turns? Ans. 1320 and 88. 



Prob. 9. Referring to the transformer in the preceding problem, what 

 are the required numbers of turns if three such transformers are to be used 

 Y-connected on a three-phase system, for which the line voltages are 6600 

 and 440 respectively? Ans. 765 and 51. 



Prob. 10. In a 110-kilovolt, 25-cycle transformer for Y-connection the 

 net cross-section of the iron is about 820 sq.cm. and the permissible maxi- 

 mum flux density is about 10.7 kl/sq.cm. What is the number of turns 

 in the high-tension winding? Ans. 6500. 



Prob. 11. The secondary of the transformer in the preceding problem 

 is to be wound for 6600 v., delta connection, with taps for varying the 

 secondary voltage within 5 per cent. Specify the winding. 



Ans. 709 turns; taps taken after the 34th and 68th turn. 



Prob. 12. Explain the reason for which a (iO-cyde transformer usually 

 runs hot even at no load, when connected to a 25-cycle circuit of the same 

 voltage. Show from the core-loss curves that the voltage must be 

 reduced to from 75 to 85 per cent of its rated value in order to have the 

 normal temperature rise in the transformer, at the rated current. 



Prob. 13. Show graphically that the wave of the Mu\. within a t 

 f riner, becomes more and more peaked when the wave of the applied 

 becomes more and more flat, and vice versa. Hint: The instantaneous 

 values of e.m.f . are proportional to the values of the slope of the curve of 

 flux. 



Prob. 14. The wave of the voltage impressed upon a transformer has 

 a 1.") permit third harmonic which flattens the wave symmetrically. Show 

 analytically that the corresponding flux wave has a ."> per rent third har- 

 in such a phase position as to make the fiuv \\.t\c peaked. 



26. The Induced E.M.F. in an Alternator and in an Induction 



Motor. Part of a revolving field alternator is >li<>\vn in Fi: 



The armature con- is stationary and has a winding placed in slots, 



which may l.e either open or half eloseil. Tin- poll- pieces ^are 



mounted on a -pider and are provided with an exciting winding. 



der i- driven l>v a pime-mover the magnetic llux 



sweeps past tin- armature conductors and induces alternating 



M them. 1 li nl.tain an e.m.f. approaching a sine 



1 For dctafli concerning the dim-rent types of armature winding* see the 

 .tut) fmental Electrical Engineering, Vol. 2, Chap. 30. 



