Winding of Alternate- Current Electromagnets. 569 



determined. This can be done by winding upon the magnetic 

 circuit an experimental coil having a known number of turns 

 w, and a known resistance r. Using this coil, measure the 

 virtual current c which passes when it is supplied at a voltage 

 v of frequency n. During the experiment the armature should 

 be fixed, say by wooden distance-pieces, in the position which it 

 will occupy in use. Then the coefficient of self-induction I of 

 the temporary coil will be 



1= tyV — cV 2 -f- \/4:7T 2 ?l 2 C 2 . 



Then I being thus experimentally determined, it follows that 

 k = l/w 2 . 



From the equation (3) we see that V, p, and k being 

 constant, there is a certain maximum number of windings 

 which must not be exceeded if we are to get the prescribed 

 number of ampere-turns of excitation ; for sin </> cannot be 

 greater than unity. If this maximum number of windings is 

 exceeded, the result will be to give fewer ampere-turns. 

 This is easily seen if equation (3) be put into the form, 



Other things being equal, the ampere-turns are inversely 

 proportional to the number of ivindings. This, at first sight, 

 seems an anomaly ; but is easily understood when we re- 

 member that the self-induction, and therefore the lessening 

 of the current, is proportional to the square of the number of 

 turns ; so that whilst we are increasing our turns we are 

 reducing our amperes in a much greater ratio. 



Having ascertained k, the only other factor to be determined 

 is sin (f>. This in most practical cases can be assumed to be 

 unity, since with the usual frequencies of supply and using 

 magnets with iron cores, there is no difficulty in keeping the 

 resistance negligibly small even when the number of windings 

 is at the required maximum, so that <f> is very nearly 90°. 

 This will be seen from the results given below obtained from 

 an actual magnet. In most ordinary cases, then, we merely 

 write 



W = Y/kpZ; (5) 



and, having calculated W, we find what current the wire will 

 have to carry from the equation 2 = ZW. If there is room, 

 and in most cases there will be ample, we may wind with 

 thicker wire than is necessary to carry the current ; but 

 there is no advantage in using thicker wire than such as 

 makes R practically negligible. 



