1 II ALTERNATING 



Ordinarily, the emf. and current vectors represent the phase 

 relations of these quantities with respect to the time. (See 

 Chap. I, Fig. 5.) 



Although 0, the flux linking the armature coil, and E', the 

 induced emf. in the coil, vary with the space position of the coil, 

 they vary also with the time. When the coil moves through 360 

 electrical degrees in space with respect to the poles, the emf. 

 wave passes through 360 electrical degrees in time. The time of 

 doing this is I// sec., where /is the frequency in cycles per second. 

 Therefore, the time required for the coil to pass through a given 

 number of electrical space-degrees is equal to the time required 

 for the emf. to pass through an equal number of electrical time- 

 degrees. For this reason a space-phase diagram and a time-phase 



emf. 



= Emf. under 



A 



FIG. 148. Vector diagram of alternator mmfs. and emfs. 



diagram may often be combined, just as the angular variation 

 of emf., Chap. I, Fig. 3, page 4, was changed to the time varia- 

 tion of emf., Fig. 5, page 6. The space-phase diagrams of 

 Figs. 147 (c) and 147 (d) may also be considered as time-phase 

 diagrams. 



Figure 148 shows the vector diagram of an alternator, in which 

 the current 7 is in phase with the induced emf. E'. As F is the 

 resultant field, E' must lag F by 90. It was shown in Fig. 138, 

 page 134, that under these conditions the armature reaction acts 

 at right angles to the resultant field, F. Therefore, the armature 

 mmf., or the armature reaction A, must have a space position of 

 90 behind the resultant field F. This brings it in phase with E', 

 and therefore in phase with the current 7, as it should be of course. 

 As F is the resultant field, it must be the vector sum of the im- 

 pressed field FI and the armature reaction field A, as shown in 

 the vector diagram. 



