188 THE TRANSFORMER. 



the voltage of a transformer when the number of the lines 

 forming the alternating field is known. 



Thus, if the leakage flux in the transformer be z lines, 

 the electromotive force of self-induction set up in a winding 

 of t turns at a frequency of current n E = z t n 4-44 x 1O 8 . 



It has already been pointed out that the strength of the 

 leakage field increases in proportion to the primary current. 

 Its actual value can only be determined by experiment or 

 previous experience of transformers of similar type. The 

 value of the electromotive force due to self-induction in the 

 primary and secondary windings respectively is approxi- 

 mately proportional to the number of turns in the windings 

 as just stated. 



Most simply the leakage effect may be shown as a single 

 electromotive force acting in the primary circuit J period out 

 of phase with the resultant primary current, as shown at e 

 in the diagram. 



In Fig. 89 the resultant current and voltage obtained 

 from the preceding case without leakage are thus shown 

 for a leakage equivalent to a voltage of 10 volts. 



A leakage field 1 of the main field is assumed, and e is 

 drawn to represent the electromotive force introduced thereby. 



The output voltage of the transformer is E' 2 < the resul- 

 tant of this voltage and the terminal voltage which would 

 exist without the leakage, and obtained as in Fig. 87. 



NOTE. In the preceding diagrams, the angle of lag in the 

 secondary circuit is shown as the angle between the phase 

 of the current and the total induced secondary voltage. It 

 must be remembered that the angle of lag between current 

 and terminal volts is the angle between C. 2 and E., v 



The following table referring to the figures just given 

 may be found convenient for reference : 



E l Voltage overcoming induced primary back 



volts. 



E Primary terminal voltage. 



C l Primary current. 



< Angle of lag of primary circuit. 



fa Angle of lag between current and total induced 



secondary volts. 

 C., E., r Angle of lag between current and secondary 



terminal volts. 

 C. 2 Secondary current. 



