164 Dr. Sumpner on the Measurement 



A current of &2 amperes was passed through a noninductive 

 resistance AB in series with the lead plates BC. The 

 voltage BC on the plates was 18*7 ; that of AB was 0'6/e, 

 while BP the minimum voltage v was 0'004/c, where k is the 

 constant previously referred to. It follows that sin 6 is 

 0*0067 and cos 6 is 0*999977. A number of similar measure- 

 ments were made with very satisfactory results. 



A small current-transformer for oscillograph purposes was 

 tested for phase-difference between primary and secondary 

 currents. This transformer was designed to reduce currents 

 in the ratio of 20 to 1, and for use on a 6000 volt circuit, for a 

 primary current not exceeding 10 amperes, and to supply a 

 secondary current to any closed circuit not absorbing more 

 than 2 volts. Noninductive resistances were put in series 

 with the primary and secondary windings, and were electrically 

 connected so as to form a point represented by in fig. ] . 

 The former for a current of 8 amperes absorbed 0*66 volt, 

 represented by OV^ The secondary resistance could be 

 tapped at various points, and the minimum voltage v repre- 

 sented by YxV 4 produced a reading of 0*50 millivolt. Allow- 

 ing for the constant 2*3, we have *00115 volt as the value of 

 v. It follows that sin is *00175, and is 0*10 degree for a 

 primary current of 8 amperes. For a primary current of 10 

 amperes was found to be 0*088 degree, and for a current of 

 7 amperes 0*114 degree. Such values of 6 yield values of 

 cos differing from unity by about one part in a million, and 

 are such that the wave-forms of primary and secondary 

 currents must correspond with almost absolute accuracy. 



Several small instrument transformers as supplied com- 

 mercially for wattmeters were tested under their normal 

 working conditions, the noninductive resistance put in the 

 secondaries being very small compared with the total secondary 

 resistance, and only absorbing a few millivolts. In one case 

 it was found that the phase-difference between the primary 

 and secondary currents of a current-transformer was 2'32 

 degrees, and in another as much as 4*2 degrees. 



A number of larger transformers £or power purposes were 

 tested for phase-differences between primary and secondary 

 voltages. In several cases the phase-difference on open circuit 

 was found to be of the order of a tenth of a degree, and 

 on full load of the order of one degree. On an inductive 

 load the phase-difference found was not so large as a rule as 

 for the same secondary current through a noninductive 

 circuit. The curve shown in fig. 4 represents the result 

 of some tests on two transformers of 3 kilowatt capacity 

 intended to work between voltages of 100 and 1000, and with 

 currents of 100 cycles per second. One transformer was 



