572 



ELECTRICAL MEASUREMENTS 



shielded, should be used at a distance of at least 6 or 8 ft. from the 

 transformer. 



Theory of the Current Transformer. To examine the theory 

 of the current transformer, transfer from Fig. 349 those parts of 

 the diagram which are shown in Fig. 352. 



FIG. 352. Diagram for current transformer. 

 Let: 



N\ and N% = number of turns in primary and secondary respectively 

 7i and 7 2 = primary and secondary currents. 



7 = total exciting current. 



IM = magnetizing component of exciting current. 



IP = power component of exciting current. *- 



0' = angle between E% and secondary current. 



/3 = phase angle of transformer. 



Reference to the figure will show that both the ratio and the 

 phase angle are dependent on the exciting current, for obviously 

 if /o were zero, I\N\ = IzNz, and /3, the phase angle of the trans- 

 former or the departure of the primary and secondary currents 

 from exact opposition, would also become zero. Such an ideal 

 transformer can never be realized, for in any case there must be 

 enough ampere-turns to give the requisite flux through the core, 

 and with the iron core, the exciting current must have an energy 

 component sufficient to account for the hysteresis and the eddy- 

 current losses. When an iron core is used, loNi may be resolved 

 into two components, the magnetizing component I M Ni along 

 the flux, and the power component I P Ni along E\. 



Referring to Fig. 352 and projecting I 2 N Z and I Ni on the line 



IiNi = #2/2 cos j8 + I Ni cos [90 - tf - - sin- 1 



ll = N* C os 8 + IM Sin (g/ + ^ + Ip COS (6> ' + - (a) 



* /2 Nl /2 



