RESISTANCES 

 A more convenient form in the case of two resistances is 



Reft = 



R1 + R2 



REAL GENERATORS 



We are now in a position to consider real generators. The definition of a 

 constant-voltage generator implies that the 'internal resistance' is zero, and 

 that of a constant-current generator that the internal resistance is infinite. 

 Real generators have internal resistances between zero and infinity, and may 

 be represented either: by an ideal constant- voltage generator in series with 

 the internal resistance r (Figure 2.5a), or by an ideal constant-current genera- 

 tor in parallel with the internal resistance r {Figure 2.5b). 



(a) 



(b) 



Figure 2.5 



If Ir in Figure 2.5b is equal to E in Figure 2.5a the two diagrams represent 

 the same thing, for if the P.D. across the terminals of the latter is measured 

 with no load resistance connected, the open-circuit voltage is clearly E. If 

 the terminals are short circuited, the short-circuit current is Ejr. If a load 

 resistance R be connected, the current through it is £■/(/• + R) and the voltage 

 across it will be E{RI(r + R)}- Similarly, in Figure 2.5b the open-circuit 

 voltage is / going through r, which is Ir. The short-circuit current is just /, 

 since it will all go through the short-circuit rather than through r. The 

 voltage across a load resistance R will be / times the effective resistance of 

 R in parallel with r, which is I{rR)j{r + R), and the current through the load 

 will be this voltage divided by R, i.e. 



_ rR 



r-\~ R 



R 



r-^ R 



Summarizing in tabular form: 



Open-circuit voltage 

 Short-circuit current 

 Voltage across load R 

 Current through load R 



8 



