ELECTRIC CIRCUIT THEORY 



363 



We now suppose that, at reference time / = 0, a short circuit is sud- 

 denly placed across ah; and require the effect of this short circuit on 

 the distributions of currents in the network. The solution of this 

 problem is based on the following proposition : 



The effect of the short circuit is precisely the same as the insertion at 

 time t = of a voltage— V(t), equal and opposite to V{t), between points 

 a and b. 



The resultant currents in the system for />() are then composed 

 of two components: — 



(1) The currents which would exist in the invariable network, in 

 the absence of the short circuit, due to the impressed source E{t). 

 These are calculable by usual methods. 



(2) The currents due to the electromotive force V{t) inserted at 

 time t = 0, between the points a and b. These are also calculable by 

 usual methods, since V(t) is itself known from the primary distribution 

 of currents and charges. 



By the preceding analysis we have succeeded, therefore, in reducing 

 the problem of a sudden short circuit, to the determination of the 

 currents in an invariable network in response to a suddenly impressed 

 electromotive force: that is, the problem to which the preceding 

 chapters have been devoted. 



The Sudden Open Circuit 



The problem of a sudden open circuit in any part of a network 

 can be dealt with in a precisely analogous manner, although the actual 

 calculation of the resultant current and voltage distribution is mathe- 

 matically more complicated. Consider the network shown in Fig. 32. 



E(t) 



let) 



Fig. 32 



Here the network is supposed to be energized by an electromotive 

 force E{t) which produced a current /(/) in the invariable network in 

 branch ab. We require the effect of suddenly opening this branch. 

 The solution of this problem depends on the following proposition. 

 The effect of opening branch ab at reference lime t = is the same as 

 suddenly inserting at time / = 0, a voltage V{t) which produces in branch 

 ah a current — I{t) equal and opposite to the current which would exist in 

 the branch in the absence of the open circuit. 



