THE TRANSFORMER. 187 



primary voltage E being the resultant of the voltage over- 

 coming the back electromotive force E v and the primary 

 "copper loss E r . 



The angle of lag of the primary circuit is again the angle 

 E C v which in this case is greater than before on account 

 of the lagging current in the secondary circuit. 



The secondary current will produce a drop of voltage in 

 phase with the current and equal to C 2 R , so that the terminal 

 voltage is the resultant of E 2 and E a E 2> . drawn parallel to 

 the current C r The terminal voltage is consequently 

 represented by E gr , and the angle of lag is the angle between 

 O, and E, . 



4r 



Two important results can be seen to follow from an 

 inductance in the secondary circuit. Firstly, the primary 

 circuit receives a correspondingly increased current-lag, 

 and secondly the ratio between the magnitude of the primary 

 and secondary voltages is seen to be affected, so that the 

 secondary voltage is always lowered by an inductive load. 

 This is very clearly seen by comparing the two diagrams, 

 Figs. 86 and 87, which have purposely been chosen with the 

 same amount of secondary current, the angle of lag in the 

 secondary circuit only being changed. 



Cose IV. Secondary circuit on load with leading current. 

 (See Fig. 88.) This case arises when the transformer supplies 

 a circuit having considerable capacity, or synchronous motors 

 which are over-excited. 



The method of drawing the diagram is the same as in the 

 preceding case, the only difference being that the current 

 line C e C 2 lies on the opposite side of E 2 . 



From the resultant voltage, it appears that the effect 

 of a slightly leading current is to increase the transformer 

 secondary voltage, so that a slightly leading current tends 

 to counteract the effect of the resistance of the windings 

 and maintain the secondary voltage more constant. 



Case V. Transformer with leakage. (See Fig. 89.) 

 The effect of leakage in a transformer is similar to the inser- 

 tion of an inductance in the circuit in which the leakage 

 occurs. It will be remembered that a self-induction in a 

 circuit gives rise to an electromotive force 90 in phase 

 behind the current in the circuit. 



The value of the electromotive force thus introduced by 

 the leakage field is given by the same formula as is used for 



