126 THE TRANSFORMER. 



flux during one-half period, and the lower arrows indicate 

 their direction after reversal of the current. 



Let Z = maximum number of lines of force produced in 



the core by the current, 

 n = periodicity of current, 

 N l = number of turns composing the winding I. con- 



nected to the alternator, 

 ^ 2 = number of turns composing the other winding 



II. 

 E 1} E z = maximum value of the voltage at the ends of 



the windings I. and II. 



The number of lines will change with the current produc- 

 ing them, and will vary harmonically, if the alternator voltage 

 supplies current having a sine wave form. 



The electromotive force generated in one turn of winding 

 = rate of change of magnetic lines -f- 10 8 . 



The maximum rate of change of the lines may be shown 

 to be 2 TT n Z by similar reasoning to that given on page 13 

 in connection with the rate of change of current. 



Hence, maximum electromotive force induced in a single 

 _, 2 Tn Z 



and the maximum voltage induced in winding (II.) having 



__ 2 n Z N., 

 N 2 turns = E 2 = - ^ -- . 



The virtual voltage corresponding to this maximum value = 



0*, or e 2 = 4-44 nZN 2 10' 8 , 



which is a fundamental formula for the voltage induced in 

 the winding of a transformer. 



But the magnetic flux passes through the windings of 

 the coil I. connected to the alternator, as well as through 

 winding II. Consequently, there will be induced a back 

 voltage in coil I., which we have previously called the 

 back electromotive force of self-induction, opposing the 

 voltage of the alternator. The value of this back voltage 

 is obviously 



ej = 4-44 n Z N l 10- 8 



since it may be calculated by the same reasoning as that just 

 given, and it is induced in a winding having N t turns. 



On account of the complete magnetic circuit of soft iron 

 on which the coil I. is wound, its self-induction is exceedingly 

 high, and the impedance of the winding is very great, and 



