84 TREATISE ON ALTERNATING CURRENTS. 



work 2^ lamps. Thus if an ampere-hour meter, or coulomb rneter, 

 is used, the consumer is the loser ; and if a watt-hour meter, 

 or energy meter, is employed, the consumer does not get value 

 for his money. The use of a series resistance is, therefore, 

 inadmissible. 



With continuous-current mains, the only alternative to a resist- 

 ance is a motor-generator ; but with an alternating-current supply, 

 the reduced voltage may be otherwise obtained : (1) by the use of 

 a choking coil, (2) by means of a step- down transformer, and (3) 

 by a motor-generator of some description. 



Of these methods the use of a step-down transformer, or a 

 choking-coil, is generally adopted. Either of these is equally 

 satisfactory to the consumer, provided the primary coil of the 

 transformer is only excited when required. The supplier prefers 

 to use transformers because the inductance is small on closed 

 secondary circuits, whereas if many choking coils are connected 

 with the supply mains the load will be highly inductive, and the 

 regulation of the generating plant will be rendered very difficult 

 (see Chap. XIII.). 



57. There are two cases for consideration : (1) that in which 

 the apparatus to be worked is non-inductive, and (2) that in which 

 it is inductive. 



CASE 1. Apparatus Non-induetive. 

 Let the K.M.S. voltage of the supply be V. 

 Let vi and i be the pressure and current required for working 

 the non-inductive apparatus. 



Let v be the pressure between the terminals of the choking coil 

 necessary for the purpose. 



We shall assume that the resistance of the choking coil is 

 negligible, so that the current i lags 90 behind 

 the P.D. between its terminals. Also, the 

 P.D. vi is in phase with i, since the apparatus 

 is non-inductive. 



Let OA (Fig. 33) represent v\ t and OL re- 

 present v. 



Then V has to supply a component OA to 

 FIG. 33. drive the current against the resistance of the 



apparatus, and another component OL' to balance 

 the E.M.F. of self-induction of the choking coil ; that is, V is 

 represented by the vector OE. 



