RESISTANCES 



To perform the reverse process, that of converting a star into the equivalent 

 delta, the equations are: 



D _ D ID I ^a^S 



Example of application — Figure 2. 15 shows an unbalanced Wheatstone 

 bridge. It is required to find the effective resistance between terminals A and B. 



Figure 2.16 



Notice that a delta is formed by the 3, 2 and 5 ohms resistances, and another 

 by the 4, 2 and 6 ohms resistances. Choose one, say the first, and convert to 

 the equivalent star {Figure 2.16). 



Rb = 



5 + 2 + 3 



5x2 



5 + 2 + 3 



_ 2X3 



'' ~ 5 + 2 + 3 



= 1-5 a 



= in 



= o-6n 



The remainder of the problem is quickly solved by the rules for series and 

 parallel resistances. 



ThevenirCs theorem 



This theorem is for finding the current in any member of a network of 

 resistances being supplied from a generator. It may be stated as follows: 

 If the resistance in question, R, be imagined to be removed, the remainder 

 of the network may be represented by a constant voltage generator of e.m.f. 

 E' in series with a resistance r', where E' is the open-circuit voltage appearing 

 across the terminals initially joined by R, and r' is the effective resistance 

 'looking into' these terminals. Thus, an equivalent circuit for the network 

 with R in place is just {Figure 2.17) and the current through R is E'l{R + r'). 



12 



