RESISTANCES AND CAPACITANCES 



CAPACITANCES ALONE 



Single capacitance 



The fundamental relationship which describes the behaviour of a capacitance 



is as follows. 



If, as a result of the effect of some generator in the circuit of which a 

 capacitance, initially uncharged, is part, a charge Q is transferred from one 

 plate, via the remainder of the circuit, to the other plate, and if the value of 

 the capacitance is C, then a difference of potential V appears across its 

 terminals, and 



Q = VC (coulombs, volts, farads) 



« 



Capacitances in parallel 



If two capacitances Q and Cg are connected in parallel to a constant direct- 

 voltage generator of e.m.f. E {Figure 3.1) then a charge Q^ is displaced round 



-0>4 — o 



^ X— a 



L 



>^ dis placed^ I Jj 



Ql displaced 



^ 



Q, +Q2 

 displaced 



Figure 3.1 



the circuit in virtue of Q, and a charge Q^, in virtue of Cg. 

 The effective capacitance Ceff for the combination is 



Total charge displaced 

 E 



_ gi+g2 _ Ci^i + Q^a 

 ~ E E 



= Ci + C2 



and in general, for n capacitances in parallel, Ceff = Cj + Cg + C3 . . . + Q. 

 If we differentiate the fundamental equation Q = VC with respect to time 



dg^dK^ 



dt dt 



dQ dV ^ 



but ^ = 7, :.i = ^c 



25 



