1 00:00:02,715 --> 00:00:04,279 [BLANK_AUDIO]. Welcome back to our continuing course in 2 00:00:04,279 --> 00:00:06,656 linear circuits. At this point, we've finished talking 3 00:00:06,656 --> 00:00:09,016 about resistive circuits, and we're going to be moving on now to reactive 4 00:00:09,016 --> 00:00:11,241 circuits. And we'll describe a little bit more 5 00:00:11,241 --> 00:00:14,860 about what that means today. Themes for this lesson where we were 6 00:00:14,860 --> 00:00:18,160 talking about capacitance is to allow you to describe the behavior of a device 7 00:00:18,160 --> 00:00:21,330 called the capacitor. By calculating the charge that's stored 8 00:00:21,330 --> 00:00:24,710 on the capacitive plates, the current that flows through the capacitor, the 9 00:00:24,710 --> 00:00:28,760 voltage across a capacitor and the capicitance of the capacitor. 10 00:00:31,240 --> 00:00:35,710 In the previous classes we've finished completing, the resisance circuits 11 00:00:35,710 --> 00:00:38,040 section. And then Dr Ferry wrapped up that section 12 00:00:38,040 --> 00:00:41,990 and then also presented an overview of this new module, the reactive circuits 13 00:00:41,990 --> 00:00:44,600 module. And then today we'll be talking about the 14 00:00:44,600 --> 00:00:47,640 first of these reactor devices capacitors. 15 00:00:47,640 --> 00:00:50,790 But, this is actually going to be discussing two different lessons. 16 00:00:50,790 --> 00:00:56,160 A, which some of the properties then physics about how these things operate. 17 00:00:56,160 --> 00:00:58,790 And then the next class well talk about the actual devices that we know as 18 00:00:58,790 --> 00:01:02,240 capacitors. The objectives for this lesson are to 19 00:01:02,240 --> 00:01:05,190 allow you to describe the construction of a capacitor. 20 00:01:05,190 --> 00:01:09,150 To find the amount of charge that's stored on a capacitor, find the current 21 00:01:09,150 --> 00:01:13,130 that goes through the capacitor, find the voltage across a capacitor. 22 00:01:13,130 --> 00:01:16,710 Calculate the capacitance of the capacitor and then explain how current 23 00:01:16,710 --> 00:01:21,310 flows through a capacitor. In short we're discussing a lot of things 24 00:01:21,310 --> 00:01:24,289 about how capacitors work. And this is similar to our resistive 25 00:01:24,289 --> 00:01:25,880 circuits section, when we talked about resistance. 26 00:01:25,880 --> 00:01:32,420 And we're going to be talking about how voltages and currents react within a 27 00:01:32,420 --> 00:01:34,370 single device. And in the next lesson, we'll start 28 00:01:34,370 --> 00:01:37,220 discussing about how they interact when we put them into a system. 29 00:01:39,110 --> 00:01:43,640 A capacitor is essentially two conductive plates that's separated by a material 30 00:01:43,640 --> 00:01:47,936 that's an insulator. Sometimes known as the dielectric. 31 00:01:47,936 --> 00:01:54,150 So here, we can see that we have th-, a top grey plate and a bottom grey plate, 32 00:01:54,150 --> 00:01:57,640 separated by, in this case, kind of a blue glassy looking thing. 33 00:01:57,640 --> 00:02:01,470 If we connect this capacitor to a voltage source, what's going to happen? 34 00:02:01,470 --> 00:02:05,850 Well the voltage source is going to be trying to move charges around because of 35 00:02:05,850 --> 00:02:10,350 this difference in charge, density that a voltage source is going to create. 36 00:02:10,350 --> 00:02:15,040 So consequently, what happens is, negative charges are placed on the bottom 37 00:02:15,040 --> 00:02:18,350 of the capacitor. And when those negative charges are 38 00:02:18,350 --> 00:02:22,220 collecting on that bottom plate. They push negative charges off of the top 39 00:02:22,220 --> 00:02:25,120 plate. Making the top plate positively charged. 40 00:02:25,120 --> 00:02:29,890 Since all of those atoms now have more protons than they have electrons. 41 00:02:29,890 --> 00:02:34,860 And so we start to see an electric field is created inside of that dielectric 42 00:02:34,860 --> 00:02:38,166 material. The insulator in between the 2 plates. 43 00:02:38,166 --> 00:02:40,800 So, this electric field can actually be quite useful. 44 00:02:40,800 --> 00:02:44,400 Because it's holding all of these charges on the plates. 45 00:02:44,400 --> 00:02:48,380 And those charges can then, in turn, be used to do something interesting. 46 00:02:48,380 --> 00:02:53,310 So if we need a whole lot of current on demand, well now we have a big well of 47 00:02:53,310 --> 00:02:57,380 current that, well, charges that can then be used to create a current. 48 00:02:57,380 --> 00:03:02,050 So if we connect a capacitor to some kind of a device, we'll see that a current is 49 00:03:02,050 --> 00:03:06,220 going to start flowing to try to equalize that charge density difference. 50 00:03:06,220 --> 00:03:08,960 On that capacitor. So we see the current that will be 51 00:03:08,960 --> 00:03:12,590 flowing from the positve to the negative. And as that happens, unlike a battery 52 00:03:12,590 --> 00:03:16,530 capacitor doesn't have any type of process that keeps this reaction going. 53 00:03:16,530 --> 00:03:21,660 Once those electrons are gone then that electric field disappates and it kind of 54 00:03:21,660 --> 00:03:29,900 finds itself to a steady state. We actually identify how much charge is 55 00:03:29,900 --> 00:03:35,630 on the capacitive plates, by using this handy equation where the charge q is 56 00:03:35,630 --> 00:03:40,630 going to be equal to c times v. And here c represents capacitance and 57 00:03:40,630 --> 00:03:43,690 we're going to be talking a little bit more today about exactly what capacitance 58 00:03:43,690 --> 00:03:46,970 means. And we see here we've got a capacitor 59 00:03:46,970 --> 00:03:50,410 connected to a voltage source and independent voltage source. 60 00:03:50,410 --> 00:03:55,540 And so the negative side of the capacitor is going to be where the negative 61 00:03:55,540 --> 00:04:00,300 terminal of the source is connected. The strength of the boltage across this 62 00:04:00,300 --> 00:04:04,570 capacitor will match. The strength of the source because that's 63 00:04:04,570 --> 00:04:06,770 what causing these charges to be moved around. 64 00:04:06,770 --> 00:04:10,040 There's some kind of pressure being applied to make this happen. 65 00:04:10,040 --> 00:04:15,380 If we remove the source then those charges are going to start to try and 66 00:04:15,380 --> 00:04:20,090 dissipate by making themselves diffused throughout the material so that there's 67 00:04:20,090 --> 00:04:26,590 no longer a difference in charge density. Just like resistance had Ohm's law to 68 00:04:26,590 --> 00:04:30,330 allow us to know how the currents and the voltages related to one another, we have 69 00:04:30,330 --> 00:04:32,670 something that's analogous for capacitors. 70 00:04:32,670 --> 00:04:35,160 But with capacitors, it's not quite so simple. 71 00:04:36,370 --> 00:04:40,350 At this point ,we're going to start seeing that time becomes more and more of 72 00:04:40,350 --> 00:04:44,600 a component. Because of the way the capacitors work as 73 00:04:44,600 --> 00:04:50,490 we place more and more charge onto the plates we see that the voltage is going 74 00:04:50,490 --> 00:04:53,440 to increase. And so voltage conseqently is an 75 00:04:53,440 --> 00:04:59,000 integration where its equal to one over c times the integral from t not to t of the 76 00:04:59,000 --> 00:05:02,190 current. With respect to time, plus whatever the 77 00:05:02,190 --> 00:05:07,570 initial voltage happens to be. We can then derive the current equation 78 00:05:07,570 --> 00:05:13,190 by taking the derivative of that, and we see that the current is equal to C dv dt. 79 00:05:13,190 --> 00:05:15,900 So as the voltage changes that lets us know how much current is flowing through 80 00:05:15,900 --> 00:05:19,440 the capacitor. So it's actually what capacitor lets us 81 00:05:19,440 --> 00:05:26,540 know is how much charge is required to get a particular electric field through 82 00:05:26,540 --> 00:05:30,040 the dielectric. So if it has a high capacitance, then 83 00:05:30,040 --> 00:05:34,390 that means that we have a whole lot of charge on that capacitor that's available 84 00:05:34,390 --> 00:05:37,870 when we apply a small voltage. So, small voltages can lead to a lot of 85 00:05:37,870 --> 00:05:40,430 current that's on demand very, very quickly. 86 00:05:40,430 --> 00:05:44,370 But we have to put those charges on there beforehand so that means that it will 87 00:05:44,370 --> 00:05:48,640 take longer to get a higher voltage. Because we have to put more charges on 88 00:05:48,640 --> 00:05:52,720 their to establish that field. When we are discussing capacitance we're 89 00:05:52,720 --> 00:05:57,100 going to be using units of ferrets which are indicated by a F and the variable 90 00:05:57,100 --> 00:05:59,655 that we're going to use in all of our equations is a C. 91 00:05:59,655 --> 00:06:03,420 It's quite simple to calculate capacitance. 92 00:06:03,420 --> 00:06:06,780 The capac, well, assuming that we have a nice geometry. 93 00:06:06,780 --> 00:06:11,070 If we have two parallel plates separated by some kind of dialectric material. 94 00:06:11,070 --> 00:06:15,980 The capacitance is simply equal to epsilon times the area of the plates. 95 00:06:15,980 --> 00:06:20,150 So the width times the length. All divided by the distance between the 96 00:06:20,150 --> 00:06:24,410 two plates. And here, epsilon is the permittivity of 97 00:06:24,410 --> 00:06:27,110 the material, of the dielectric material, or that insulator. 98 00:06:28,270 --> 00:06:32,170 You might remember from before, we talked about the permittivity of free space. 99 00:06:32,170 --> 00:06:38,120 And that's how willing a vacuum is to allow an electric field to be established 100 00:06:38,120 --> 00:06:40,915 in it. As you change the material, the 101 00:06:40,915 --> 00:06:44,780 permitivity changes. And that's one of the major things that 102 00:06:44,780 --> 00:06:50,150 allows us identify how much capacitance it has, or how much charge is required to 103 00:06:50,150 --> 00:06:53,170 create an electric field through that dialectic material. 104 00:06:54,900 --> 00:06:59,040 Normally though, when we're talking about these perpetuities, the values that were 105 00:06:59,040 --> 00:07:03,040 using are very, very, very small. As we mentioned, the permittivity of free 106 00:07:03,040 --> 00:07:08,010 space is 8.85 times 10 to the negative 12 [INAUDIBLE] per meter. 107 00:07:08,010 --> 00:07:12,290 And so instead of using the permittivity of the material directly, often what 108 00:07:12,290 --> 00:07:17,250 we'll do is use an epsilon R, which is the relative permittivity of that 109 00:07:17,250 --> 00:07:19,750 material. And then we multiply epsilon R times 110 00:07:19,750 --> 00:07:22,422 epsilon ot. Define the true permittivity. 111 00:07:22,422 --> 00:07:26,040 So you we give you some idea of the order of these permittivities. 112 00:07:26,040 --> 00:07:30,180 We have a table here to kind of give you some kind of sense. 113 00:07:30,180 --> 00:07:33,950 Eric behaves almost like a vac, vacuum, its relative permittivity is 114 00:07:33,950 --> 00:07:38,424 approximately one. Teflon is a better insulator as 2.1. 115 00:07:38,424 --> 00:07:43,310 A paper 3.9 and it starts to go up as we get down to things like water. 116 00:07:43,310 --> 00:07:45,479 Water actually has a fairly high permittivity. 117 00:07:45,479 --> 00:07:48,138 78.5. But in all of these cases the 118 00:07:48,138 --> 00:07:51,876 permittivity does vary somewhat based upon things like temperature. 119 00:07:51,876 --> 00:07:54,787 there are also some different properties of materials. 120 00:07:54,787 --> 00:07:58,129 And, when we're talking about things like Paper. 121 00:07:58,129 --> 00:08:01,390 There's a lot of variety that you can find within the paper. 122 00:08:01,390 --> 00:08:05,690 So, even between different areas of the same material, that permittivity can 123 00:08:05,690 --> 00:08:09,890 actually change quite a bit. Now, we've been talking a little bit 124 00:08:09,890 --> 00:08:12,492 about the current that's flowing through a capacitor. 125 00:08:12,492 --> 00:08:16,190 But I almost mentioned that, in between the 2 plates is an insulator. 126 00:08:16,190 --> 00:08:19,730 And so it doesn't really want to let current go through. 127 00:08:19,730 --> 00:08:22,775 So how is this current flowing through the capacitor? 128 00:08:22,775 --> 00:08:27,280 Well, it's not really flowing through the capacitor, not a lot of the electrons are 129 00:08:27,280 --> 00:08:31,700 actually crossing that gap, but what we see is if we push an electron under the 130 00:08:31,700 --> 00:08:37,070 bottom plate, this way. Then what's going to happen it's going to 131 00:08:37,070 --> 00:08:42,860 be pushing away a negative charge on the opposite of the plate because like 132 00:08:42,860 --> 00:08:47,010 charges are going to repel one another. And so as a negative charge gets pushed 133 00:08:47,010 --> 00:08:53,203 away from the other plate, it leaves a positive ion, an atom that has an extra 134 00:08:53,203 --> 00:08:57,000 proton because that electron's been moved so it's no longer electrically neutral, 135 00:08:57,000 --> 00:09:02,600 so it becomes positively charged. And so what we see, if we don't really 136 00:09:02,600 --> 00:09:07,380 care that it's a capacitors, an electron comes in one side, and then an electron 137 00:09:07,380 --> 00:09:10,250 comes out the other side. It's a different electron, but we really 138 00:09:10,250 --> 00:09:12,820 don't care. And so this is the way that we say a 139 00:09:12,820 --> 00:09:16,290 current flows through a capacitor even though none of these elements are 140 00:09:16,290 --> 00:09:20,514 actually crossing through that dielectric. 141 00:09:20,514 --> 00:09:26,380 And so that way we see this current. To summarize, we identify that something 142 00:09:26,380 --> 00:09:28,930 by how these capacitors work. And so now you should have a little bit 143 00:09:28,930 --> 00:09:32,260 of understanding of how these parallel plates are working; as we apply voltage, 144 00:09:32,260 --> 00:09:35,460 what happens to the charges? And we were able to calculate that charge 145 00:09:35,460 --> 00:09:39,800 on a capacitor using that q is equal to c times v. 146 00:09:39,800 --> 00:09:42,500 We showed the relationship between current and voltage on the capacitor, 147 00:09:42,500 --> 00:09:46,590 which is a differential. or based on time. 148 00:09:46,590 --> 00:09:48,990 So that time derivative of voltage allows us to see the current. 149 00:09:48,990 --> 00:09:52,930 And then we calculated this capacitance. And explained what we mean when we say 150 00:09:52,930 --> 00:09:54,715 the current is flowing through the capacitor. 151 00:09:54,715 --> 00:09:59,900 In the next class, we'll talk about capacitors as circuit devices, and we 152 00:09:59,900 --> 00:10:03,980 will look at the behavior of how these capacitors behave in an actual circuit 153 00:10:03,980 --> 00:10:07,396 environment. Until then