RESISTANCES AND CAPACITANCES 



produced across A-B of the form of Figure 3.7; there is an initial step of 

 magnitude IR, followed by a steady rise in voltage of rate //C. This follows 

 straightforwardly from our findings for a resistance and a capacitance con- 

 nected to a constant-current generator separately. 



vab 



Figure 3.7 



Series R and C connected to a constant direct voltage generator 



In this case the solution is not quite so simple. In Figure 3.8, if the genera- 

 tor is of e.m.f. E, then clearly 



E=Vji-\-Vc 



=^iR + \ dV 



-'Hli 



dt 



Close at 



Figure 3.8 



This is a differential equation having the solution, /= (EIRje'^^^^K The 

 voltage across the resistance, Vj^, is iR = Ee^^'^^, and the voltage across 

 the capacitance, Vq, must be E minus this, E{\ — e~^'^^) (Figure 3.9). 



Figure 3.9 



For the non-mathematically minded reader, a verbal description of what 

 is happening is as follows. When the generator is first connected, the capaci- 

 tance is uncharged, and has no potential difference across it; therefore the 



28 



