ELECTROMOTIVE FORCE AND CURRENT 23 



given, where the meaning of the vectors is not otherwise 

 evident. Vectors indicating electromotive forces are shown 

 with thin arrow-heads. Vectors representing currents have 

 thick black arrow-heads. Also vectors referring to magnetic; 

 flux have arrow-heads with double barb. 



The diagram Fig. 8 represents the instantane^fe condition 

 of current and voltage at the instant when the voltage has 

 its maximum positive value, since the line E is shown 

 horizontal and directed towards the right ; it will thus have 

 its maximum horizontal projection at this moment. The 

 line C, representing the current is drawn 52^ later in phase, 

 the angle C E being 52J, and the direction of rotation 

 being clockwise. The instantaneous value of the current 

 is obtained by drawing a vertical line C N and measuring 

 the length of N on the scale. It is seen to be 15-3 amperes, 

 which corresponds with the value measured on the curve in 

 Fig. 7 for the same phase. 



Resultant of Two Vectors. Fig. 9 shows by means of 

 vectors the component and resultant electromotive forces 

 of Fig. 7; the instant for which the diagram is drawn is not 

 the same as in the former figure. The two voltages E r and E 1 

 are drawn at right angles, since they differ in phase by 90. 

 The lettering will make obvious the identity of the vectors. 

 The scale is the same as for Fig. 8. 



As before, the instantaneous values could be found by 

 drawing verticals through the rotating end of each line. 

 The student should identify the phase and instantaneous 

 values of Fig. 9 in Fig. 7. 



In this diagram it will be found that if the two component 

 voltages E r E { are taken to be two sides of a parallelogram 

 the completed parallelogram would have the vector E as its 

 diagonal. That is, the resultant electromotive force would 

 be represented in magnitude and phase by the diagonal of a 

 parallelogram of which the two components formed the sides. 



That this must always be true follows from the following 

 consideration. Since the instantaneous value of the 

 resultant electromotive force is the sum of the values at each 

 instant of the component electromotive forces, the horizontal 

 projection of the vector representing the resultant must 

 always equal the sum of the projections of the components, 

 because the horizontal projections are instantaneous values 

 of the quantities. 



