4-A] SERIES AND PARALLEL CIRCUITS. 105 



that is, to cause a current / to flow through a resistance R, an 

 in-phase electromotive force equal to RI is required. 



9. Significance of Vectors. In developing the theory of vec- 

 tor diagrams for alternating current quantities, the vectors rep- 

 resent the maximum values of quantities which vary according 

 to a sine law. In applying these diagrams, however, the vectors 

 are usually drawn to represent the effective (or virtual) values, 

 as measured by ammeter and voltmeter, the effective value of 

 a sine wave being JV 2 times its maximum value.* Furthermore, 

 vectors are used for currents and electromotive forces which do 

 not vary exactly as a sine law, although the results in these cases 

 are not, in general, theoretically correct.f In drawing vector 

 diagrams, it is implied, therefore, that the currents and electro- 

 motive forces have wave forms which are sine waves or may be 

 represented by, equivalent sine waves of the same effective values. 

 The phase difference 0, between equivalent sine waves for cur- 

 rent and electromotive force, is determined by the relation: 

 cos = power f actor = W -f- EL 



10. Direction of Rotation. Counter-clockwise rotation is 

 usually taken as the direction of rotation of alternating current 

 vector diagrams, and this convention will be here followed. 



By considering a diagram as making one complete revolution 

 (360) in one cycle, the projections, from instant to instant, of 

 the various lines of the diagram upon any fixed line of reference 

 will be proportional to the instantaneous values of the quantities 

 represented by those lines. By reversing all diagrams as in a 

 mirror, the corresponding diagrams, for clock-wise rotation will 

 be obtained. 



11. Electrical Degrees. In alternating current vector dia- 

 grams, " angle " is a measure of time, 360 indicating the time 



* See Bedell and Crehore's Alternating Currents, p. 38, and other text- 

 books. 



t (Qa). Compare 60-64; for further discussion, see references given 

 in gb, Exp. 5-C. 



