0:00:00.560,0:00:05.940 In the last video we worked out the step response of an RC circuit and now we're 0:00:05.940,0:00:11.250 going to look at a real example. This is the step response, the total response to our 0:00:11.250,0:00:16.379 circuit to a step input. And what does this look like? So I'm going to move down a 0:00:16.379,0:00:22.039 little bit. We'll make up a circuit and we'll do a real example here. 0:00:40.600,0:00:52.270 Let's say we do a step and the step goes from 0.2 volts up to say 1.1 volts, 0:00:52.270,0:01:03.640 and let's let R equal 1k ohm, and let the capacitor equal 4 microfarads. 0:01:03.640,0:01:10.479 So now let's plug these values over here into our solution and see what 0:01:10.479,0:01:19.810 we get. Now first I'm going to work out RC. RC is equal to 1 K ohm times 4 microfarads. 0:01:19.810,0:01:29.200 And what is that equal? K is +3 and micro is -6, so 1 times 4 is 4 0:01:29.200,0:01:39.820 and plus 3 minus 6 is times 10 to the minus 3 and that is in seconds so that's 0:01:39.820,0:01:49.259 equal to 4 milliseconds. Now let's plug the rest of our values in here. V of T, 0:01:49.259,0:02:00.460 the total response or the step response, equals V0, 0.2, minus Vs, that's the 0:02:00.460,0:02:16.329 step voltage, 1.1, times e to the -t over 4 milliseconds plus Vs. Vs 0:02:16.329,0:02:25.360 is 1.1. So I went ahead and I plotted this using a computer and 0:02:25.360,0:02:30.000 we'll see how close this comes to what we sketched earlier. 0:02:35.000,0:02:44.260 So here's VT, or the step response, the total response of our RC network to a step voltage. 0:02:44.260,0:02:52.359 The step voltage is here in rose color, and it goes from 0.2 volts up 0:02:52.359,0:03:02.290 to, oh I got it wrong, 1.2 volts. Let's change that to the right number, 1.2, 1.2. 0:03:02.290,0:03:07.000 And this is what it looks like. And if you go back and compare this to what we 0:03:07.000,0:03:11.720 saw what we sketched at the beginning it'll look pretty similar. So the output 0:03:12.220,0:03:16.900 voltage, the voltage on the capacitor here, 0:03:19.100,0:03:26.980 starts at V0, which is 0.2. It ends up at Vs, which is 1.2, in this case. And that's the forced 0:03:26.980,0:03:33.300 response up here, and in between it did that smooth exponential curve.