22 ELECTROMOTIVE FORCE AND CURRENT. 



force represented. On a complete diagram this should be 

 indicated as in Fig. 8, thus <x = 50, indicating a frequency 

 of 50 cycles per second, so that the vector C must be taken 

 to rotate 50 times per second. 



20 40 , 60 



SCALE OF VOLTS & AMPERE$. ^ - 50 

 FIG. 8. VECTOR DIAGRAM OF VOLTAGE AND CURRENT. 



By means of the convention just described, a single line 

 is sufficient to indicate the maximum value and manner of 

 variation of a periodic quantity, and also to indicate its 

 phase and instantaneous value at any moment. This method 

 further enables us to show the relation between two such 

 quantities which have the same periodicity, but which may 

 have any relative magnitude and phase. The quantities 

 need not necessarily be of the same nature. Thus, for instance 

 the relation between a current and a voltage may easily be 

 shown on the same diagram by two different lines. 



The scale to which the lines have been drawn should be 

 indicated whenever use is made of vector diagrams. 



The difference in phase between the various quantities 

 is measured directly as degrees of angle between the lines 

 representing them in the vector diagram, 360 being one 

 complete period. 



By way of illustration, Fig. 8 has been drawn to represent 

 the current and voltage of the circuit given by the curves 

 in Fig. 7. Consequently the vector C represents 25 amperes 

 on the scale of amperes, this being the maximum value of the 

 current. Similarly E represents 49 volts, the maximum 

 value of the voltage. The angle C E between the vectors 

 is 52 J, which was found to be the angle of lag of the circuit. 



In order to distinguish between lengths representing 

 electromotive forces and those representing currents, the 

 following distinction will be observed in all figures subsequently 



