RESISTANCES AND CAPACITANCES 



If y is allowed to operate a few more times, it becomes evident that : 



and that 



] 



Now, when we were considering the series C and R connected to the 

 constant-current alternator, in order to find the potential difference across the 

 combination we had to add the voltage across the resistance and the voltage 

 across the capacitance vectorially, 'at right angles'. With the help of y we 

 can deal with this easily, for by convention resistance is regarded as being 

 measured along the axis of real positive numbers, and capacitive reactance 

 along the axis of negative imaginary numbers ; thus the expression for the 

 impedance is just R — jXq. Let us now applyy to solving a practical problem. 



Series R and C connected to a constant-voltage alternator 

 With the arrangementof F/^Mrei.22,if the generator output is represented by 



© 



\ 



'in 



Figure 3.22 

 vector Fja the current which flows round the circuit is represented by the vector 



R-jXa 

 and the potential difference it produces across R is 



VinR 



and across C is 



Thus 



and 



Kin 

 Vr 



Fin R -jXc 



Notice that these expressions may be written down by inspection; for the 

 network forms a potentiometer which is only different from the potentio- 

 meters we have so far dealt with in that one of the elements is reactive 



34 



