CHAPTER VIII. 



The Calculation of Electric Currents in Reactive Circuits Series Circuits 

 Parallel Circuits Mutually Reactive Circuits. 



THE APPLICATION OF VECTOR ALGEBRA TO ALTERNATING-CURRENT 



PROBLEMS. 



4O. Before attempting to read this and subsequent chapters, the 

 student is urged to make himself thoroughly conversant with the 

 contents of the foregoing chapter on Vector Algebra. All that is 

 necessary for a comprehensive study of its subsequent applica- 

 tions is there given, and the method is so much simpler and 

 more instructive than the more ponderous methods involving the 

 calculus and differential equations, that no apology is necessary 

 for its introduction. After thoroughly mastering the method, 

 which will require a concentrated effort for but a short time, 

 subsequent reading will be simplicity itself, and the student 

 should experience little or no difficulty in solving most alternating- 

 current problems by its help. One feature, perhaps, more than 

 any other stamps the method of vector algebra as being par 

 excellence the method for the solution of alternating-current pro- 

 blems ; that is, that while it obviates a profound mathematical 

 knowledge, it does not in any way save thought. Each problem 

 must be thoroughly viewed and understood in its physical aspects 

 before the method of vector algebra can be applied. In the 

 following applications we shall endeavour to emphasize the value 

 of the method by a judicious selection of problems, and by de- 

 ducing the vector equations from physical considerations only. 



41. Before proceeding to apply the method to specific pro- 

 blems, we must recall three important propositions. 



Proposition 1. The maximum value of the induced 

 E.M.F. due to self-induction in a circuit is pLI, where / is the 

 maximum value of the current in the circuit, L is the self-in- 

 duction of the circuit, and p = 2irn, where n is the frequency of 



