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tive if it is flowing in the positive direction; negative if flowing in the 

 negative direction. 



An e.m.f. or a voltage between two points is positive if the potential 

 increases in the positive direction between the two points; negative 

 if the potential increases in the negative direction. (It may be noted 

 that this convention makes the sign of a voltage the same as the sign 

 of that e.m.f. which could be inserted between the two points without 

 producing any effects in the network.) 



CHAPTER X 



Introduction to the Theory of Variable Electric Circuits ^ 



In the preceding chapters it has everywhere been assumed that the 

 networks are invariable: that is to say, that the constants and con- 

 nections of the network do not vary or change with time. In many 

 important technical problems, however, we wish to know, not merely 

 what happens when an electromotive force is applied to an invariable 

 network, but the effect of suddenly changing a circuit constant or of 

 introducing a variable circuit element. In the present chapter we shall 

 show that this type of problem can be dealt with by a simple extension 

 of the methods discussed in the preceding chapters. 



The simplest and at the same time one of the most technically 

 important problems of this type is the effect of sudden short circuits 

 and sudden open circuits on an energized network or system. This 

 type of problem will serve as an introduction to the more general 

 theory. 



The Sudden Short Circuit 



Consider the network shown in Fig. 31. 



Fig. 31 



This network, which for generality is supposed to consist of two parts 



A and B, indicated schematically, is energized by an electromotive 



force £(/) which produces a voltage V{t) between the points ab. 



The voltage V(t) is calculable by usual methods from E(t) and the 



constants and connections of the network, supposed to be specified. 



9 The material in this chapter is largely- taken from a paper by the writer on 

 "Theory and Calculation of Variable Electrical Systems," Phys. Rev. Feb. 1921. 



