RC natural response example (3 of 3)

We just derived what the current is and the voltage. These are both the natural response of the RC. Now, what I did is I went ahead and I plotted out this using a computer, just using Excel to plot out what these two expressions look like. Let me show you that.

So, let's do a real quick example here with real values, just to see how this equation works. We'll say that this is 1,000 ohms; that's our resistor, and we'll say C is 1 microfarad. What we want to work out is R * C, which equals 10^3 ohms * 10^-6 farads, and that equals 10^(-3) seconds or 1 millisecond. That's the product of R and C.

I forgot the voltage; let's say we put two volts on this capacitor to start with like that. Now, we can say V of T equals V KN, which is 2 volts, times e^(-t/1 millisecond). That's our natural response for this particular circuit.

Now, let me show you what that looks like. This is V of T on this side equals 2 e^(-t/1 millisecond). You see it starts at 2 volts and then sags down as we predicted, and that's an exponential curve.

Then over here on this side, as we said before, it starts out at zero. The current in the capacitor is zero, and as soon as we throw open that switch, the charge charges over through the resistor. This is the equation here: I of T equals 2 volts over 1000 e^(-t/RC) or e^(-t/1 millisecond).

So, this is what we call the natural response of an RC circuit, and you'll run into this in almost every circuit you ever build.