# RC Circuit Pulse Excitation

Discussion in 'Homework Help' started by blah2222, Jan 23, 2011.

1. ### blah2222 Thread Starter Well-Known Member

May 3, 2010
565
33
Hi, I just have a quick question regarding a simple circuit with a resistor and capacitor both in series with a voltage source. The only trick to this question is that the voltage source is a pulse excitation where it can be anything.

The easy part is deriving the differential equation for the capacitor voltage:

$\frac{dV(t)}{dt} + \frac{V(t)}{RC} = \frac{Vs(t)}{RC}$

From this we use the integrating factor method to bring us to this:

$V(t)*exp{\frac{t}{RC}} = \frac{1}{RC}\int{Vs(t)*exp{\frac{t}{RC}}dt}$

Thing is, how do I use this if I'm given an input Vs(t) that is not a "normal" function of time.

Hope my question was clear, I'll try to post up an example of an input, soon.
JP

2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Integration doesn't need a continuous or smooth argument. For example this is valid: $\int^{\inf}_{-inf} \delta (t-\tau) \cdot f(t) d t = f(\tau).$