REAL GENERATORS 



The whole process is much quicker to do than to describe. If, instead of 

 being told the total current supplied to the network we had been told the 

 e.m.f. to which it had been connected, we would have worked out the total 

 current by dividing the effective resistance of the network, 3*33 ohms, into 

 the e.m.f. 



The class of network which can be solved along these lines may be dej&ned 

 in the following way. If for every point where a current divides into two 

 fractions there is another point at which the same two fractions are reunited, 

 then the network may be solved by the rules for series and parallel resistances. 

 Thus, Figure 2.7 is soluble because the currents which divide at Fmeet again 

 at G, and those which part company at AC coalesce once more at BD. 



A network which does not fulfill these conditions is the unbalanced 

 Wheatstone bridge {Figure 2.12). Current divides at A, flows down the 

 two arms of the bridge and meets at B. If current is flowing along C-D, 

 clearly the two currents leaving A are not in the same ratio as those 

 meeting at B. The classical way of solving this problem, and its elaborations, is 

 to resort to Kirchhoff''s laws, setting up and solving a number of simultaneous 

 equations. We shah not do this, but have recourse instead to two powerful 

 weapons which follow from Kirchhoff"'s laws. They are the theorem of 

 Thevenin and the star-delta transformation. 



v?^ 



^ 



B 



Figure 2.12 



Figure 2.13 



Figure 2.14 



The star-delta transformation 



If three resistances have the configuration of Figure 2.13 they are said to 

 form a 'mesh' or 'delta'. It can be shown that an equivalent arrangement is 

 that of Figure 2.14, called a 'star', provided the resistances comprising the 

 star are related to the mesh resistances in the following manner : 



Rr,^ 



Rb = 



i?v- 



i?li?3 



