INSTRUMENT TRANSFORMERS r,7:* 



But ft is a small angle; its cosine is, therefore, very nearly unity, 

 and the second member on the right-hand side of the equation 

 is virtually a correction term. 

 Hence : 



Pofio - 7l ^ 2 j_ IM sin e ' + J f cos *' 



= 7^ ~ ]\T T approximately. 



The expression for the phase angle is determined as follows. 

 From the diagram, 



loNi sin 90 - B' - ft - sin~ l ~ 



tan = - tl 



IzNz cos j8 



_ / JVi cos (0' + ft - 7,JVi sin (0' + ft 



wr , cos 



As is a small angle, 



Nif/M cos 0' IP sin 0'~| 

 P = -TT- r approximately. 



i V 2 L J 2 



In the practical case 7 2 leads /i reversed. This is important 

 in power measurements. 



The dependence of the ratio and the phase angle on the proper- 

 ties of the core are clearly shown in (a) and (b) . Evidently both 

 I M and IP should be reduced to a minimum if both the ratio and 

 the phase angle are to be made as nearly independent of the 

 secondary current and the character of the secondary load as 

 possible. 



In the current transformer J varies with the saturation of the 

 core, i. e., with consumers' load current. To reduce I M the core 

 must be of high permeability and of large cross-section. // is 

 rendered small by choosing for the core an iron of small hysteresis 

 loss and working the iron at a very low flux density. The im- 

 pedance of the instruments forming the load should be small so 

 that the requisite secondary e.m.f. is furnished by a small flux. 



As there is iron in the magnetic circuit the current wave form 

 in the secondary cannot be an exact reproduction of that in the 

 primary. But with periodic phenomena the distortion, while 

 measurable by refined methods, is so small that it is of no prac- 

 tical moment even though the wave form be very complicated. 



Owing to the action of the iron, however, large currents of a 

 transient nature, such as occur in short-circuit tests of fuses, 



