RESISTANCES AND CAPACITANCES 



Thus if a capacitance, initially uncharged, be connected to a direct constant- 

 current generator of output /, the potential difference across the capacitance 

 grows linearly with time, at a rate dV/dt = IjC (Figure 3.2). 





Figure 3.2 

 Capacitances in series 



If two capacitances Q and C^ are connected in series with a generator of 

 constant current /, the rate of growth of potential difference across Q is 

 (dKe^)/(d/) = //Ci and across Q is (dVcJIidt) = //Cg (Figure 3.3). 



Figure 3.3 

 Therefore the rate of growth of potential difference across the combination 



IS 



/ / /I 



7r + 7r = / 7^ + 



cj 



Cj C^ \Ci ^^1 



If the effective capacitance of Q and C^ in series is Cen, the rate of growth 

 of potential difference across Ceff when charged by a current / is 



/ 



Ceff 



therefore 



Ceff 



/ ^ 



.Q 



1 1 1 



so 7; — ^ ~r^ ~\~ 1^ 



and in general for n capacitances in series is 



J 1 J_ 1 



Ceff Ci C2 C3 



A more convenient form for two capacitances in series is Ceff = (C-^C2)I 

 (Q + C2). 



1 



Capacitance connected to constant-voltage alternator 



If a capacitance be connected to an alternating voltage, constant-voltage 

 generator, or constant-voltage alternator (Figure 3.4), of output v = Fsin cot, 

 the current through the capacitance is 



/ = C dvfdt 



d(FsincoO 



^^ dt 



= coCF cos a>t 

 26 



