6.2 The RC Circuit
KCL for the single-node-pair prototype RC circuit below yields the differential equation (DE): Cdv(t)/dt + v(t)/R = iS(t) which can be written as dv(t)/dt + v(t)/(RC) = (1/C)iS(t) which is (again) of the generic form: dx(t)/dt + x(t)/T = f(t) where the time constant T = RC
So, similar to the RL circuit, the generic solution is:
v(t) = [v(0) - vSS(0)]e-t/(RC) + vSS(t) (which is text Equation 6.42 on p. 223)