ELEMENTARY ELECTRICAL CIRCUIT 



The potential-divider and potentiometer 



Resistances connected as in Figure 2.3a are said to be in 'series', and the 

 total resistance in the circuit isR^ + i?2- IJ^ electronics we often wish to reduce 

 a potential diflference to some fraction, either fixed or variable. If a current / 

 flows through R^ and R2, it produces a potential difference of IRj^ across R^ 

 and IR2 across R2, making a total of I(Ri + R^) across the pair. In the 

 potential divider the total potential difference /(i?i + R2) is thus divided into 

 two fractions of which one, IR2, is made use of at the output terminals be. 

 The transmission factor of the device is 



^out 



IR. 



Ro 



in 



/(i?i + R2) {R^ + R2) 



If the transmission factor is to be made variable, the device is called 2i potentio- 

 meter {Figure 2.3b) in which a 'tap' connection can be moved up and down a 

 single resistance, dividing it into two parts. {R^ + R^ is now a constant and 

 the transmission factor is proportional to R^. 



in 



(a) 



(b) 



Figure 2.3 



Figure 2.4 



Resistances in parallel 



Resistances connected as in Figure 2.4 are said to be connected in parallel 

 or shunt. The current in R^ is EfR^ and in R2 is £'//?2- Therefore, with resis- 

 tances in parallel the current divides inversely as the ratio of the resistances. 

 The total current /tot is EjR^ + EJR2. The effective resistance of the com- 

 bination is thus 



F F 



^^^" = /tot = T^ 



/?1 /?2 



Dividing top and bottom by E, we find that for two resistances in parallel 



/ 

 R.n = y--7 



/?1 /?2 



and in general for any number of resistances 



/ 



Ren 



Rl i?2 





