WEBVTT 00:00:00.170 --> 00:00:04.035 >> Okay. Now let's talk about what happens to voltage and current, 00:00:04.035 --> 00:00:07.790 and we first turn on a voltage source let's say we first took up the battery, 00:00:07.790 --> 00:00:11.760 it's going to start putting charges on top of this plate, 00:00:11.760 --> 00:00:15.615 which is then going to force charges away from this plate and again this flow of current. 00:00:15.615 --> 00:00:17.820 Current starts to flow immediately. 00:00:17.820 --> 00:00:23.370 Its largest at the start and gradually as the charges fill up on his plate, 00:00:23.370 --> 00:00:25.830 there'll be no current at the end when the plates are all full. 00:00:25.830 --> 00:00:28.470 So, current begins to start immediately 00:00:28.470 --> 00:00:31.725 and is largest at the beginning and then falls down to zero. 00:00:31.725 --> 00:00:37.250 Meanwhile, the current starts 00:00:37.250 --> 00:00:40.345 immediately but then when the plates are full it goes to zero. 00:00:40.345 --> 00:00:42.540 So, what does that look like the current? 00:00:42.540 --> 00:00:46.430 Here is a picture of an interesting circuit where we have a switch that's going to 00:00:46.430 --> 00:00:50.510 take this 10-volt battery and turn it on to start charging this capacitor. 00:00:50.510 --> 00:00:53.825 We know that the current is dq dt that that's also 00:00:53.825 --> 00:00:57.346 equal to the capacitance times the change in voltage with respect to time. 00:00:57.346 --> 00:01:00.545 So, as I turned this on, let's see what's going to happen. 00:01:00.545 --> 00:01:02.090 When I first turn it on, 00:01:02.090 --> 00:01:04.640 it's going to go up to its peak current and then it's 00:01:04.640 --> 00:01:08.370 going to gradually go down to zero as the plates get full. 00:01:08.500 --> 00:01:13.190 In fact, it's peak current is going to occur up 00:01:13.190 --> 00:01:17.140 here when the capacitor is effectively a short circuit. 00:01:17.140 --> 00:01:19.300 So, look right here when we first started, 00:01:19.300 --> 00:01:22.020 all the current can go into that faster. 00:01:22.020 --> 00:01:24.310 At the very beginning when we had a big change, 00:01:24.310 --> 00:01:26.905 this capacitor acts like a short circuit. 00:01:26.905 --> 00:01:29.130 So, what will the current be? 00:01:29.130 --> 00:01:32.044 It will be this voltage divided by that resistance, 00:01:32.044 --> 00:01:35.100 and in fact, right there, that's what it is. 00:01:35.100 --> 00:01:37.650 Is simply what everything at time t equal to zero, 00:01:37.650 --> 00:01:39.730 and then we have this exponential decay. 00:01:39.730 --> 00:01:43.030 The speed of the decay depends on something that we call the time constant, 00:01:43.030 --> 00:01:47.705 tau that is equal to R times C for a series resistor capacitor circuit. 00:01:47.705 --> 00:01:49.230 If I have for example, 00:01:49.230 --> 00:01:50.465 R is one kilo ohm, 00:01:50.465 --> 00:01:52.490 C is one microfarad and this voltage, 00:01:52.490 --> 00:01:54.820 this is exactly what my currents would look like, 00:01:54.820 --> 00:01:58.960 starting out at VS over R and ending at zero. 00:01:58.960 --> 00:02:02.690 The time constant tells us that as this exponential decreases, 00:02:02.690 --> 00:02:05.480 it will reach 36 percent of its original value, 00:02:05.480 --> 00:02:08.860 at the time constant tau equals RC. 00:02:08.860 --> 00:02:12.150 Okay. Now what happens when we first turn on the voltage. 00:02:12.150 --> 00:02:14.720 Well, originally there are no charges on the top plate, 00:02:14.720 --> 00:02:16.475 there are no charges on the bottom plate, 00:02:16.475 --> 00:02:20.705 and so the total voltage across here would start out as zero. 00:02:20.705 --> 00:02:23.660 But as we gradually add up all of these charges, 00:02:23.660 --> 00:02:25.885 then there's going to be a large voltage at the end. 00:02:25.885 --> 00:02:31.430 So, the voltage is the integral of the current over time with the capacitance inverted. 00:02:31.430 --> 00:02:34.085 So, right here's my case. 00:02:34.085 --> 00:02:37.115 I'm going to be integrating the current over time. 00:02:37.115 --> 00:02:38.495 This is what it looks like. 00:02:38.495 --> 00:02:42.110 My voltage starts out at zero and it ends up that Vs. 00:02:42.110 --> 00:02:45.580 The voltage is one over the capacitance times the integral of time, 00:02:45.580 --> 00:02:50.675 and if you look at that, that's going to be Vs times 1 minus e to the minus t over tau. 00:02:50.675 --> 00:02:52.685 Again, it's the same time constant. 00:02:52.685 --> 00:02:59.115 So, the voltage reaches 66 percent of its value at the time constant RC. 00:02:59.115 --> 00:03:03.360 So, here's the answer to what does a capacitor do to a voltage and current? 00:03:03.360 --> 00:03:06.215 With the current plot we looked at and here's the voltage plot. 00:03:06.215 --> 00:03:08.120 Steady state would be long time, 00:03:08.120 --> 00:03:10.760 like after the switch has been closed for a long time, 00:03:10.760 --> 00:03:14.960 and that would say there would be no current and that there would be a large voltage. 00:03:14.960 --> 00:03:17.840 At time t equal to zero when there is a very big change, 00:03:17.840 --> 00:03:19.670 the capacitor acts as a short circuit. 00:03:19.670 --> 00:03:22.340 The time t equal to infinity when it's all charged up, 00:03:22.340 --> 00:03:24.590 it acts like an open circuit. 00:03:24.590 --> 00:03:27.160 Now what are the implications of that? 00:03:27.160 --> 00:03:30.140 When we have something that we want to charge and discharge, 00:03:30.140 --> 00:03:33.810 instead of being able to do a square wave like they might have liked, 00:03:33.810 --> 00:03:36.140 we always end up with some stray capacitance and make 00:03:36.140 --> 00:03:40.120 our square wave looks like this charging, discharging plot. 00:03:40.120 --> 00:03:42.255 How do we use capacitors? 00:03:42.255 --> 00:03:45.080 Here are two examples where we use them for energy storage. 00:03:45.080 --> 00:03:48.620 This disposable camera for example has two batteries and a capacitor 00:03:48.620 --> 00:03:52.310 inside in order to make the flash that you use when you take a picture. 00:03:52.310 --> 00:03:55.280 The capacitance between the clouds and the earth 00:03:55.280 --> 00:03:58.685 is what creates the ability for lightning to strike. 00:03:58.685 --> 00:04:03.605 We can also use capacitors to stabilize power for example to the reduce ripple. 00:04:03.605 --> 00:04:06.740 Here's a case where we've put in a power supply and let's suppose that 00:04:06.740 --> 00:04:10.060 sometimes it was a little more than nine volts and sometimes it was a little less, 00:04:10.060 --> 00:04:13.310 but that our circuit over here wants exactly nine volts. 00:04:13.310 --> 00:04:16.790 In that case, this capacitor can take a little bit of that 00:04:16.790 --> 00:04:20.975 away when it's too high and return a little bit back, when it is low. 00:04:20.975 --> 00:04:25.565 The capacitor effectively storing the excess and release it when it is needed. 00:04:25.565 --> 00:04:29.020 Now let's talk about low pass and high pass filters. 00:04:29.020 --> 00:04:31.145 A low pass signal is going to allow 00:04:31.145 --> 00:04:34.775 a constant value to go through but not the high frequency noise. 00:04:34.775 --> 00:04:37.040 So, here's a series RC circuit, 00:04:37.040 --> 00:04:40.250 where remember that if I have a change, 00:04:40.250 --> 00:04:44.575 a fast changing thing that this thing acts like an open circuit. 00:04:44.575 --> 00:04:49.540 So, it allows the low frequency to go through but not the high frequency. 00:04:49.540 --> 00:04:50.960 Here's another example. 00:04:50.960 --> 00:04:53.060 What does this look like without the capacitor? 00:04:53.060 --> 00:04:55.100 Looks like an inverting amplifier. 00:04:55.100 --> 00:04:58.280 Now let's suppose that we tried to send a DC value through. 00:04:58.280 --> 00:04:59.720 Well, the DC value, 00:04:59.720 --> 00:05:01.940 this capacitor still acts like an open circuit. 00:05:01.940 --> 00:05:05.390 So, it just acts like an inverting amplifier that you've always seen before. 00:05:05.390 --> 00:05:07.450 The low pass signal goes through, 00:05:07.450 --> 00:05:11.585 but now what if I wanted to send a grasp changing a high frequency signal. 00:05:11.585 --> 00:05:14.315 In that case, the capacitor would act like a short circuit. 00:05:14.315 --> 00:05:16.145 I'll be shorting out my R2. 00:05:16.145 --> 00:05:23.855 Remember what the amplification for inverting amplifiers, 00:05:23.855 --> 00:05:30.455 remember that the gain is equal to minus RF divided by RS, 00:05:30.455 --> 00:05:34.130 and then in this case the RF is R2, 00:05:34.130 --> 00:05:36.640 but if I made RF equal to zero, 00:05:36.640 --> 00:05:38.130 then my game would be zero. 00:05:38.130 --> 00:05:40.935 So, the high frequency signal that will come out with the zero. 00:05:40.935 --> 00:05:44.610 The capacitor allows the low frequency to go through this circuit, 00:05:44.610 --> 00:05:49.975 goes through R2 that takes the high frequency through here and basically equals to zero. 00:05:49.975 --> 00:05:53.115 This allows the capacitor to work as an integrator. 00:05:53.115 --> 00:05:55.580 Notice here's the RC circuit right here. 00:05:55.580 --> 00:05:59.180 It's taking this square wave and it's producing this output. 00:05:59.180 --> 00:06:00.995 Remember what integration does? 00:06:00.995 --> 00:06:02.980 It finds the area under the curve. 00:06:02.980 --> 00:06:06.200 When I first made my step up the area is zero, 00:06:06.200 --> 00:06:08.630 and gradually as I'm adding up, adding up, 00:06:08.630 --> 00:06:10.250 adding up the area of the curve, 00:06:10.250 --> 00:06:12.325 it builds up the maximum voltage. 00:06:12.325 --> 00:06:14.090 When I take a negative value, 00:06:14.090 --> 00:06:15.860 it starts subtracting off that value. 00:06:15.860 --> 00:06:17.990 So, there's no charging discharging though. 00:06:17.990 --> 00:06:23.140 I can literally use this capacitor circuit to integrate signals that are coming in. 00:06:23.140 --> 00:06:26.775 Here's a high pass filter design or DC block. 00:06:26.775 --> 00:06:31.835 In this case, notice I've just switched the location of my capacitor and my resistor. 00:06:31.835 --> 00:06:34.680 If I were sending a DC signal through, 00:06:34.680 --> 00:06:38.495 this capacitor it would look like an open circuit and my output voltage would be zero. 00:06:38.495 --> 00:06:41.960 Nothing will come out, but if I had a high frequency signal from 00:06:41.960 --> 00:06:46.475 this capacitor would act like a short circuit and the full voltage would come out. 00:06:46.475 --> 00:06:49.235 Now here's my inverting amplifier again. 00:06:49.235 --> 00:06:53.780 Remember, that the gain is equal to minus RF which is R2 in 00:06:53.780 --> 00:06:58.725 this case divided by RS which is R1. 00:06:58.725 --> 00:07:02.340 Well, if I have a DC signal my RS is infinity, 00:07:02.340 --> 00:07:04.650 and so my full voltage comes out. 00:07:04.650 --> 00:07:09.035 If I have an AC or very high frequency signal, I have a short circuit, 00:07:09.035 --> 00:07:13.680 and that means that I get no frequency, no signal out. 00:07:13.680 --> 00:07:18.950 So, high pass signals come through but low pass signals do not. 00:07:18.950 --> 00:07:21.395 That allows me to do differentiation. 00:07:21.395 --> 00:07:24.260 That means that I want to emphasize the changes. 00:07:24.260 --> 00:07:25.755 Here's an up and here's a down. 00:07:25.755 --> 00:07:27.180 If I did the derivative, 00:07:27.180 --> 00:07:32.210 I would see this and I will see that for this is what my capacitor does, 00:07:32.210 --> 00:07:37.970 it seems a little but there's my first step and here's my second step. 00:07:37.970 --> 00:07:41.700 This is the differentiation of the square length. 00:07:41.920 --> 00:07:45.200 So, basically we have covered these four topics. 00:07:45.200 --> 00:07:46.525 What is capacitance? 00:07:46.525 --> 00:07:48.480 How does it relate to current and charges? 00:07:48.480 --> 00:07:50.090 How do the various parameters of 00:07:50.090 --> 00:07:53.690 the capacitor matter and what does it do to a voltage and a current? 00:07:53.690 --> 00:07:56.880 Thank you very much for your attention.