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Current time:0:00Total duration:3:40

- [Voiceover] In the
last video, we worked out the step response of an RC circuit, and now we're gonna
look at a real example. So, this is our answer,
this is the step response, the total response to our
circuit, to a step input. And what does this look like? Well, I'm gonna move down a little bit. We'll make up a circuit and
we'll do a real example here. Let's say we do a step, and the step goes from .2 volts up to, say 1.1 volts. And let's let R equal one K, ohm. K, ohm. And let the capacitor
equal four microfarads. So now let's plug these values
over here into our solution and see what we get. Now, first I'm gonna work out RC. RC is equal to one K, ohm times four microfarads. And what does that equal? K is plus three. And micro is minus six. So one times four is four. And plus three minus six is times 10 to the minus three. And that is in seconds, so that's equal to four milliseconds. Now, let's plug the rest
of our values in here. V of T. The total response, or the step response equals v naught, .2, minus V, S, that's the step voltage, 1.1, times e to the minus t over four milliseconds plus V, S. V, S is 1.1. So I went ahead and I plotted this using a computer, and we'll
see how close this comes to what we sketched earlier. So here's V, T. Or, the step response, the total response of our RC network to a step voltage. The step voltage is here in rose color. And it goes from .2 volts up to, ooh, I got it wrong. 1.2 volts, let's change
that to the right number. 1.2, 1.2. And this is what it looks like. And if you go back and
compare this to what we saw, what we sketched at the beginning, it'll look pretty similar. So, the output voltage, the
voltage on the capacitor here, starts at V naught, which is .2, it ends up at V, S, which
is 1.2 in this case, and that's the forced response up here. And in between, it did that
smooth exponential curve. That's what the step response
of an RC circuit looks like.