18 ELECTROMOTIVE FORCE AND CURRENT. 



This has been done in Fig. 7, and is shown as the dotted 

 curve Ej whose maximum value is 27rwLC = 27rx50x 

 005 x 25 = 39-3 volts, where n = periodicity = 50 cycles per 

 second. 



The curves drawn in Fig. 7 represent completely the. 

 conditions which usually exist in an alternating circuit. 

 These may be briefly recapitulated as follows : 



A current c (Curve C) to produce which requires the 

 application of an electromotive force varying in the same 

 manner as, and simultaneously with, the current in order to 

 overcome the resistance of the circuit. This electromotive 

 force (Curve E r ) is always numerically equal to the product 

 of c x R where R is the resistance of the circuit. 



Further, the variation of the current calls forth an electro- 

 motive force opposing this variation (Curve Ei). This 

 electromotive force is numerically equal to c L, where c 

 is the rate at which the current varies (measured in amperes 

 per second), and L is the coefficient of self-induction of the 

 circuit. The curve representing voltage overcoming the 

 latter electromotive force is similar in character to the 

 curve of current, but a quarter of a period earlier in phase. 



The ratio -- is sometimes called the time constant of the 

 circuit. 



Resultant Electromotive Force. In the previous paragraph 

 it was explained that two electromotive forces are required 

 to maintain an alternating current, viz., one electromotive 

 force in phase with the current to produce the passage of the 

 current. This may be called the resistance electromotive 

 force, and is the electromotive force which would be required 

 in a continuous-current circuit to maintain the flow of the 

 current. 



A second electromotive force produces the variation of 

 the current, and may be called the inductance electromotive 

 force. This is only required in a circuit in which the current 

 changes, and constitutes the main difference between alter- 

 nating and continuous current problems. The inductance 

 electromotive force is a quarter of a period earlier in phase 

 than the resistance electromotive force, that is, the curve 

 is displaced to the left in the diagrams. 



An alternator must supply to a circuit sufficient voltage 

 to be equivalent to both of these electromotive forces if 



