ELECTROMOTIVE FORCE AND CURRENT. 19 



an alternating current is to be maintained. The actual 

 voltage supplied by the alternator at any instant must be 

 equal to the sum of the two individual voltages. The variation 

 of the voltage of the alternator may consequently be plotted 

 as a curve, the height of which at each point is equal to the 

 sum of the ordinates of the voltages overcoming ths two 

 opposing electromotive forces. This curve has been obtained 

 in Fig. 7 from the resistance electromotive force and induc- 

 tance electromotive force, and the resultant single voltage 

 of the alternator (Curve E) has at each point a height equal 

 to the sum of the heights of these curves. 



It is to be observed that (1) this curve is again similar in 

 character to the previous curves ; (2) its maximum value (49 

 volts) is greater than that of either of the component electro- 

 motive forces, but is less than the sum of the two; (3) that 

 the resultant electromotive forces is intermediate in phase 

 between the two component curves. 



Angle of Lag. A further most important result is to be 

 noted from an inspection of the curves just given, viz., that 

 the curves representing the current and the resultant voltage 

 (i.e., the current and total voltage in a circuit) are not in 

 phase with each other. In the curves given in Fig. 7, it will 

 be seen that the curves of current and total voltage pass 

 through zero at points situated -145 period or 52^ apart. f 

 The angle between these curves, which is most conveniently 

 measured as the angle on the- horizontal scale of the curve 

 between the points at which they pass through their zero value, 

 is the angle of phase difference between current and voltage. This 

 angle is called the angle of lag of the circuit if the current 

 passes through zero after the voltage, or the angle of lead if 

 the current passes through zero before the voltage. The 

 current always lags behind the voltage, except in cases where 

 the circuit possesses electrostatic capacity or supplies over- 

 excited synchronous motors conditions discussed later on. 



The angle of lag of a circuit is of great practical importance, 

 and depends upon the nature of the resistances and other 

 apparatus forming the circuit. 



The student cannot be too careful to familiarise himself 

 with the reasons for the fact that in all alternating circuits 

 possessing self-induction there is a difference of phase be- 

 tween current and voltage. 



+ A complete period is always taken as corresponding to 3GO Q , or an angle 

 of 2T in circular measure. 



