THE USE OF COMPLEX QUANTITY. 



95 



A fifth step is necessary when it is desired to calculate power, which is equal to 

 the numerical value (effective) of voltage times the numerical .value (effective) of 

 current times the cosine of phase difference. When current and voltage are found in 

 terms of their components, for example, when : 



and 



then the power may be easily calculated by the formula : 



This equation does not of course involve j in any way, but in using this equation 

 especial care must be taken to give to each component its proper algebraic sign. 



46. Coils in parallel. A given alternating current / divides between two coils 

 connected in parallel as shown in Fig. 87. It is required to find 7j and 7 2 , each 

 in terms of /, r v r v x l and x v The general relation between 7, 7 lf 7 2 , and the 

 voltage E between the branch points is shown in the clock diagram Fig. 88. The 



Fig. 87. 



Fig. 88. 



equations are somewhat simplified if we introduce the conductance g and the suscep- 

 tance b of each circuit according to the definitions given in Art. 42, namely : 



