ALTERNATING-CURRENT COMMUTATOR MOTORS 359 



x f = 2 irfLf and x a = 2 x/L , respectively, where / is the frequency 

 of the impressed e.m.f. 



Fig. 338 shows the vector diagram for the motor. 



? Ir f a Current J 



FIG. 338. Vector diagram of a single-phase series motor. 



ox = I = current in field and armature. 



oa = Ir f = e.m.f. consumed by the resistance of the field. 



ab = Ix f = e.m.f. consumed by the reactance of the field. 



be = Ir a = e.m.f. consumed by the resistance of the armature. 



cd = Ix a = e.m.f. consumed by the reactance of the armature. 



dk = & = e.m.f. generated in the armature due to rotation, in 

 phase with the field flux and, therefore, in phase with 

 the current, neglecting the hysteretic lag. 



ok = E = impressed e.m.f. 



cos kox = cos = load power factor. 



cos dox = cos <J> 8 = power factor at start. 



Taking the current as the real axis the relation between the 

 current and the impressed e.m.f. can be expressed in rectangular 

 coordinates as 



E = & + I(r a + rf)+jI(x a + x f ) . . . (333) 



and taking absolute values 



I(r a + r,)p + [I(x a + x f ) \\ . . (334) 

 At standstill 



E = I V(r a + rtf + (x a + x f Y . . . (335) 

 and the current is 



7 = , JL= (336) 



V^ + TV^ + OCa + Z/) 2 



Full voltage can usually be impressed on the motor at standstill 

 without causing any injury since the current is limited by the large 

 impedance. 



