152 ALTERNATING CURRENTS 



transformers. In this method it is assumed that the apparatus under 

 test behaves as if it possessed a definite constant resistance, and a 

 definite constant self-inductance, under all possible conditions of load. 

 These assumptions are practically quite correct in the case of trans- 

 formers, but by no means so in the case of alternators. 



The values of the resistance and self-inductance are determined 

 by the short-circuit test. This consists in short-circuiting the apparatus 

 the armature of the alternator in the one case, the secondary of the 

 transformer in the other through an ammeter of negligible resistance 

 and self-inductance, and adjusting the exciting current in the one 

 case, and the primary p.d. in the other, until the full-load current is 

 obtained.* A second test, the open-circuit test, is then carried out. 

 The apparatus is open-circuited, and a voltmeter connected across 

 the armature in the one case, the transformer secondary in the 

 other. The reading of this voltmeter is noted when the exciting 

 current in the one case, and the primary p.d. in the other, has 

 the same value as it had in the short-circuit test. Then the ratio 



voltmeter reading in open-circuit test ,, . , , 



:p 5_ -JL gives the impedance of the ap- 



ammeter reading in short-circuit test 



paratus, and in the method about to be explained this impedance is 

 assumed to remain constant under all conditions of load. 



We have next to analyze the impedance into its resistance and 

 reactance components. The resistance of the alternator armature will 

 be approximately equal to its resistance as measured by means of 

 continuous currents (owing to eddy currents, an apparent increase of 

 resistance may be produced amounting, perhaps, to 20 per cent, in 

 extreme cases). In order to find the equivalent resistance r of the 

 transformer,! due to the resistances r\ and r 2 of its primary and 

 secondary respectively, we notice that, since for a given winding 

 space and given mean length of turn, the resistance varies as the 

 square of the number of turns, a resistance r\ in the primary is 



/S \ 

 equivalent to a resistance r\ ( ) a in the secondary, Si and S 2 denoting 



\Di' 



the primary and secondary turns respectively. Thus the total equivalent 



/S \ 2 

 r esistance component of the transformer impedance is r 2 -f- TI ( ~- ) . 



The reactance component is given by \/(impedance) 2 (resistance) 2 . 

 Since the resistance component seldom exceeds t^th of the reactance 

 component, its exact determination involving the allowance to be 

 made for eddy currents is not a matter of very great importance.} 



* See, however, 90. 



t Referred to its secondary circuit. 



J It may be noted that the alternator reactance here considered is practically the 

 total, reactance of the armature (not merely its leakage reactance, 85), i.e. it is 

 practically identical with the value of the reactance which would be obtained if the 



