44 ELEMENTS OF ELECTRICAL ENGINEERING. 



Proof. During i////-th of a second a given armature con- 

 ductor sweeps past a field pole, from a to b, Fig. 22, and cuts <E> 

 lines of force. This conductor therefore cuts lines of force at an 

 average rate which is equal to <> H- ijpn t or <&pn lines of force 

 per second, and this is the average electromotive force in the 

 given conductor while it is moving from a to b, Fig. 22 ; also 

 this is the average electromotive force per conductor in all the 

 conductors between a and b at any instant. Now, there are Zip' 

 conductors * in series in each path between the brushes, and 

 since Qpn is the average electromotive force per conductor, there- 

 fore Zip' x Qpn is the electromotive force between the brushes. 

 That is, E a = p3?Znlp' , in which E a is, of course, expressed in 

 abvolts. 



Equations (21) apply to bipolar or multipolar machines, and to 

 machines having ring or drum armatures with any kind of wind- 

 ing except open-coil windings, and these equations give the elec- 

 tromotive force induced in the windings between the brushes, 

 provided the brushes are at the neutral points as shown in Fig. 22 

 and as explained in article 5 I . 



31. Field excitation of generators. Some very small gener- 

 ators, such as the " magnetos, " which are used for ringing tele- 

 phone call bells, are provided with field magnets of hardened 

 steel, which are permanently magnetized. Large generators and 

 motors, on the other hand, are always provided with electrically 

 excited field magnets (electromagnets). 



Separate excitation and self -excitation. The field magnet of 

 an alternator must be excited by direct current, usually from an 

 outside source, as stated in Art. 27. f The field magnets of cer- 



* The conductors which constitute a given path are always distributed evenly over 

 the space ab, Fig. 22, so that the average electromotive force per conductor for all 

 the conductors of a path is the same as the general average for the whole armature. 

 In the simple ring- wound armature, /=/' and the conductors which at any instant 

 lie between the points a and b, Fig. 22, constitute one path. 



f In the so-called composite field alternators this separate excitation is supple- 

 mented by a direct current supplied by the alternator itself through a rectifying com- 

 mutator. 



