[R2K2D2]

Ah, great question! It's great to hear some more complex aspects of circuits and circuit analysis. Alright, so we can basically break things up in to two main categories...resistive circuits and RC/RL circuits. If we take a nodal/loop equation for a resistive circuits, we get algebra equations (often we use matrices to solve these). Now for RC/RL circuits we have interconnections of sources, resistors, capacitors, and inductors. Inductors and capacitors have differential or intgral voltage and/or current relationships. Since your question pertains specifically to RC capacitors, I'll just talk about that. So, when we have a Capacitor, we have an integral relationship. This is because it takes time to charge up and discharge the capacitor, which brings in calculus (YAY!!!). When one capcitor is there in a circuit with a resisor and sources we get a first order RC circuit. Here Lamda will be represented by ' L '. These circuits will have an exponential response which means it will be proportional to A + Be^Lt for constants A, B, and L. So, if we have a source and a resistor in series with a capacitor we will hvae some initial capcitor voltage Vc(0-) where the 0- describes the instant just before zero. If we take a loop equation here, we get Vs(t) = RIc(t) + Vc(t). Because Ic(t) = C*dVc(t)/dt and if we substitute this into the first eqn, we get Vs(t) = RC * dVc(t)/dt + Vc(t). or... dVc(t)/dt + 1/RC*Vc(t) = 1/RC*Vs(t). So, this equation shows us that the derivative of the capacitor voltage plus 1/RC times the capacitor voltage equals 1/RC times the source voltage. So, in the circuit that has a voltage source and a resistor in series with a capacitor, we can show the capacitor current Ic(t) as the differential equation:
dIc(t)/dt + 1/RC*Ic(t) = 1/R * dVs(t)/dt.

So I have thrown a lot of equations and stuff, kinda complex stuff. Essentially it is based on differential equations which is some upper level math. Basically, a capacitor is going to be used in order to create some type of signal. I guess if you take a look at a tv, this can give a good general example. In the TV transmitter u have a signal which is essential in creating the image on the screen. If you have an oscilloscope a timing signal is used that acts as a tibe base which lets you see measured input signals as a function of time. When you hook this up to the TV, you will get a certain output on the oscilloscope. In the perfect conditions, the voltage will increase in a linear fashion with the time until it gets to a region where it will all of a sudden go to zero, which starts this chain process over again. This voltage region corresponds to a fixed unit of time. The linear voltage goes up and then acts as an electronic "second" hand, ticking off the smaller units of time. The linear increase in the voltage is approximated by the linear part of an exponential response in the RC circuit. When the voltage measured across the capacitor reaches a certain range, the capacitor is quicky discharged to zero. Once this happens, another switch reactivates the circuit and starts the process over. Basically, the capacitor will set a certain type of output which we want to use to reproduce. Via differential equations, we can calculate certain aspects of the RC circuit.

I know that this was rather long, lengthy and maybe not totally clear. I hope I was able to help even a little bit and at least gave you a little clearer answer/background. Yes it's complex, but once you really take a look at it, it's not tooo bad. Let me know if you have any more questions.