20 TREATISE ON ALTERNATING CURRENTS. 



If E is the maximum value of e 



E = nABp (3) 



and 



e = E sin pt (4) 



Such an E.M.F. is called Alternating 1 because during each 

 revolution of the coil it rises from the value zero to a positive 

 maximum, then passes through the value zero and becomes 

 negative, attaining a negative maximum numerically equal to 

 its positive one, and then rises to the value zero again. 



Fig. 3 is a graphic representation of equation (4). 



If the extremities of the revolving coil are connected to two 

 collecting rings mounted on the axis of rotation and insulated 

 from each other so that the coil can be revolved between the poles 

 of an electro-magnet, we have an alternating-current 

 generator, or an alternator. 



An alternating current may be supplied to an external circuit 

 by means of two brushes making rubbing contacts with the col- 

 lecting rings. 



The simplest form of alternator consists of either a drum or 

 a ring armature which rotates between the poles of separately 

 excited field magnets. A diagrammatic representation is given in 

 Fig. 4. 



FIG. 4. 



In such a two-pole machine the E.M.F. developed passes 

 through a complete cycle of changes or alternation once every 

 complete revolution of the revolving part. 



As it is necessary for such purposes as electric lighting to have 

 not less than about forty complete alternations per second, a two- 

 pole alternator would be impracticable except in very small 

 machines. If, instead of having but two poles, four alternately 



