274 



ALTERNATING CURRENTS 



the p.d. Draw EP, making an angle with 0V such that angle 

 EOV = a = TT - tan- ireactance * At O erect a perpendicular OC 



resistance 



to EP, and on 0V describe an arc 

 having its centre on OC. Then it 

 is evident from the construction 

 that the angle contained in the 

 segment is a. Again, angle POA 

 = TT _ a _ /YOA ; and since we 

 must have /VOA + a + = rr, it 

 follows that /POA = <J>. Hence 

 /POA is the angle of lag of current 

 behind p.d., and PO = OA cos $ is 

 proportional to the power absorbed 

 by the motor. 



The torque of the motor is pro- 

 portional to OA 2 . 



A very simple construction for 

 the speed may be obtained as 

 follows. AV is proportional to 

 speed X field (since AV represents 

 the e.m.f. due to the rotation of the 

 armature), i.e. 



AV oc speed x OA 

 or 



i 

 speed GC- 



Draw VS || OP, and produce 

 OA to intersect VS at S. Then 

 the triangles OAV and OVS are 



FIG. 166. Circle Diagram of Series Motor. 01 - -la-, Ofl ^^ AV _ . X 



similar, u nictu - . c\\f' 



since 0V is constant, we see that 



speed oc VS 

 and VS will, to a certain scale, represent the speed of the motor. 



* The value of tan d> = 



?? is easily obtained from COB $, the latter value 



resistance 



being measured by means of a wattmeter, an ammeter, and a voltmeter when the motor 

 armature is held fast. 



