RESISTANCES AND CAPACITANCES 



The solution is 



^ R \ CRJ 



giving for the voltage across the resistance 



.« = £..-«™(l-^) 

 and for the voltage across the capacitance, 



CR 



Resistance and capacitance in series with a generator whose output is of the 

 form e = Ee-"^\\ - tjCR) 



We repeat the above process once more, supplying our series circuit with 



Figure 3.11 



a voltage waveform similar to v^ in Figure 3.10 {Figure 3.11). By a similar 

 procedure we find 



v^=^E.e-''^^(l-^+ '' ^ 



CR^ IC^R^j 

 and 



Vc = E.e-^'^4^ + 



\CR ' 2C^Ry 



Graph 7 is a plot of Vj^ in the three cases, i.e. 



Case 1 . Voltage step after passage through one RC network. 



E . e-'/c-R 

 Case 2. Voltage step after passage through two RC networks. 



Case 3. Voltage step after passage through three RC networks 



,/pr. / 2/ t^ \ 



E . e-^l^^ 1 - t;^ + 



CR ' IC^R^J 

 Notice that the response in cases 2 and 3 is oscillatory. 



Resistance and capacitance in series with constant-current alternator 

 When a resistance and a capacitance are connected in series to a generator 



30 



