1 00:00:02,250 --> 00:00:06,230 Hello, I'm Nathan Parrish, and welcome back to our course on linear circuits. 2 00:00:06,230 --> 00:00:09,460 Today we're going to be talking about resistance. 3 00:00:09,460 --> 00:00:13,035 And so the aim for this lesson is to help you identify the relationship between 4 00:00:13,035 --> 00:00:16,299 current and voltage in resistive materials. 5 00:00:18,320 --> 00:00:21,488 This is the first lesson, [INAUDIBLE] content lesson of the second module, 6 00:00:21,488 --> 00:00:25,610 which covers resistive circuits. And so the first thing we're going to be 7 00:00:25,610 --> 00:00:30,390 covering, is this idea of resistivity, and what that actually means. 8 00:00:30,390 --> 00:00:32,910 The objectives for this lesson are to, first of all, we're going to define what 9 00:00:32,910 --> 00:00:36,740 resistance is, then we'll calculate conductance and resistance. 10 00:00:36,740 --> 00:00:40,016 And then we'll use Ohm's Law to be able to solve for currents and voltages and 11 00:00:40,016 --> 00:00:44,210 resistances, based upon the information that we have. 12 00:00:44,210 --> 00:00:47,590 We'll also calculate the resistance of a material, using both its electrical 13 00:00:47,590 --> 00:00:51,915 properties as well as its geometry and dimensionality of the device. 14 00:00:51,915 --> 00:00:55,540 So, the first thing we're covering is Ohm's Law. 15 00:00:55,540 --> 00:00:58,872 Ohm's Law is something that you'll end up using a whole lot through circuits, it's 16 00:00:58,872 --> 00:01:02,330 one of the most essential things for you to understand. 17 00:01:02,330 --> 00:01:05,802 And it gives us a way of describing the relationship between a current and a 18 00:01:05,802 --> 00:01:09,836 voltage. So, Ohm's Law basically states that, the 19 00:01:09,836 --> 00:01:14,115 voltage is equal to a current times this thing called a resistance. 20 00:01:14,115 --> 00:01:17,131 But in order for us to make sure our answers are consistent, reference 21 00:01:17,131 --> 00:01:21,780 instructions, again, come into play and were very important. 22 00:01:21,780 --> 00:01:25,112 So, when we have it in what's sometimes referred to as the passive configuration, 23 00:01:25,112 --> 00:01:29,248 or when the current arrow's pointing from the plus to the minus. 24 00:01:29,248 --> 00:01:33,360 Then we just say v is equal to i times R. However, if the arrow is pointing from 25 00:01:33,360 --> 00:01:37,820 the minus to the plus, we flipped their respective reference directions. 26 00:01:37,820 --> 00:01:40,840 And so to keep our values consistent, we multiply by a negative one. 27 00:01:40,840 --> 00:01:44,360 So, in this case, v is equal to negative i times R. 28 00:01:44,360 --> 00:01:47,274 keep close track of your reference directions or you'll find yourself 29 00:01:47,274 --> 00:01:53,320 getting weird answers. Resistance is essentially the ratio of 30 00:01:53,320 --> 00:01:58,275 the voltage to the current. We measure it in units of Ohms, which is, 31 00:01:58,275 --> 00:02:02,869 again, named after a scientist. And one ohm is equal to one volt per 32 00:02:02,869 --> 00:02:08,038 ampere, or one volt per amp. When we are using equations, we're going 33 00:02:08,038 --> 00:02:12,981 to represent it with a capital R. And so we can also say that R is equal to 34 00:02:12,981 --> 00:02:16,474 v divided by i. There's another way we can look at this 35 00:02:16,474 --> 00:02:18,424 problem. We can also look at it as, how willing is 36 00:02:18,424 --> 00:02:21,670 this material, to let current flow through it? 37 00:02:21,670 --> 00:02:25,481 We call this conductance, conductance is measured in units of Siemens. 38 00:02:25,481 --> 00:02:28,829 And this is named after the same Siemens as the man that started the company 39 00:02:28,829 --> 00:02:32,535 Siemens. We represent Siemens with a capital S, 40 00:02:32,535 --> 00:02:36,510 which one Siemen is equal to one amp per volt. 41 00:02:37,760 --> 00:02:41,390 But sometimes when you're writing out your, your equations, it's difficult to 42 00:02:41,390 --> 00:02:45,020 distinguish a lower-case s representing seconds and a capital S representing 43 00:02:45,020 --> 00:02:48,644 Siemens. So, sometimes people go back to the older 44 00:02:48,644 --> 00:02:53,108 version, which was the Mho. And a Mho is basically an ohm backwards, 45 00:02:53,108 --> 00:02:56,890 so it will be represented by an upside-down omega. 46 00:02:56,890 --> 00:03:00,130 They're both equal to the same thing, one amp per volt. 47 00:03:00,130 --> 00:03:04,930 When we're doing calculations, we'll represent these values with a capital G. 48 00:03:04,930 --> 00:03:10,050 And so, G then is going to be equal to the ratio of the current to the voltage. 49 00:03:10,050 --> 00:03:12,820 And again, remember that reference directions here do matter. 50 00:03:14,370 --> 00:03:18,210 So, what is it that gives these materials this resistance? 51 00:03:18,210 --> 00:03:20,530 What are the properties that make this happen? 52 00:03:20,530 --> 00:03:23,302 And, so, to better understand this, what we're going to do is we're going to look 53 00:03:23,302 --> 00:03:27,244 at the periodic table of the elements. When looking at the periodic table if 54 00:03:27,244 --> 00:03:30,142 you've taken chemistry you know that all of these atoms want to be like noble 55 00:03:30,142 --> 00:03:34,004 gases. They somehow want to have a full outer 56 00:03:34,004 --> 00:03:37,889 shell. And so, electrically, the same thing 57 00:03:37,889 --> 00:03:40,328 holds true. So, to help us understand, we're going to 58 00:03:40,328 --> 00:03:43,790 look at a few different examples of some elements. 59 00:03:43,790 --> 00:03:46,300 And, see what kind of electrical properties they show. 60 00:03:46,300 --> 00:03:49,320 First of all, we look at lithium and chlorine. 61 00:03:49,320 --> 00:03:53,875 So, lithium is right here. And chlorine is right here. 62 00:03:53,875 --> 00:03:56,622 Chlorine's pretty close to be a noble gas argon. 63 00:03:56,622 --> 00:04:00,300 But it has seven electrons in its outer shell. 64 00:04:00,300 --> 00:04:04,740 It wants to get one more, like this, to make it like argon. 65 00:04:06,020 --> 00:04:10,550 But when it does that, first of all, it gets a charge, a negative 1 charge. 66 00:04:11,780 --> 00:04:15,320 But because it It so wants to be like a noble gas, it's somewhat willing to 67 00:04:15,320 --> 00:04:21,270 accept electrons. And so it's something of a conductor. 68 00:04:21,270 --> 00:04:24,510 lithium, lithium wants to become like neon. 69 00:04:24,510 --> 00:04:28,270 And to do that it needs to get rid of that outer electron. 70 00:04:29,640 --> 00:04:33,820 So, when that happens, it gets a positive one charge because there's more protons. 71 00:04:33,820 --> 00:04:36,280 In the nucleus of the atom than electrons in the shell. 72 00:04:39,000 --> 00:04:44,005 And so, it really comes down to, how tied are the atoms to their electrons, that 73 00:04:44,005 --> 00:04:48,940 lets this get some concept of their resistance. 74 00:04:48,940 --> 00:04:53,378 Another one we're going to look at is copper, which is a really good conductor. 75 00:04:53,378 --> 00:04:57,718 Copper's right here. Now, it has a lot of electrons in this 76 00:04:57,718 --> 00:05:01,765 shell here, that it's not particularly tightly bound to. 77 00:05:01,765 --> 00:05:05,671 But that electron in particular, it, it would like to get rid of because it's 78 00:05:05,671 --> 00:05:11,146 just all by itself in this outer shell. And when it does that, again because it's 79 00:05:11,146 --> 00:05:14,270 losing an electron, it's going to get a positive charge. 80 00:05:14,270 --> 00:05:18,950 But because this electron is just so far out and copper is so weakly bound to it, 81 00:05:18,950 --> 00:05:23,590 copper ends up becoming a very good conductor. 82 00:05:23,590 --> 00:05:28,230 As are, things like silver and gold. All of the things in this, this chain 83 00:05:28,230 --> 00:05:31,012 here. There's another class, that we'll look 84 00:05:31,012 --> 00:05:35,780 at, silicon. And silicon is right here. 85 00:05:37,080 --> 00:05:39,330 Now, you'll see that it has four electrons in it's outer shell. 86 00:05:39,330 --> 00:05:43,856 So, it could either get four more, to make it like argon or it could get rid of 87 00:05:43,856 --> 00:05:48,980 four to make it like neon. It's kind of torn in the middle. 88 00:05:48,980 --> 00:05:52,945 So, consequently, this is not a particularly good conductor, this class 89 00:05:52,945 --> 00:05:58,397 of materials is known as semiconductors. Because the way, how willing they are to 90 00:05:58,397 --> 00:06:02,877 accept or cast off electrons, is very closely related to the other materials 91 00:06:02,877 --> 00:06:07,885 that are around them. And these semiconductors end up becoming 92 00:06:07,885 --> 00:06:12,520 a very important class of atoms, when dealing with electrical circuits. 93 00:06:16,310 --> 00:06:19,162 As we were talking about electrons flowing through these systems, the way 94 00:06:19,162 --> 00:06:22,060 that electrons flow through systems is that they kind of get passed from one 95 00:06:22,060 --> 00:06:26,347 atom to another. So, in this system, we'le have a bunch of 96 00:06:26,347 --> 00:06:31,744 purple atoms and a little blue electron. As we send the little electron in, this 97 00:06:31,744 --> 00:06:36,595 first atom absorbs the electron, and becomes negatively charged. 98 00:06:36,595 --> 00:06:40,920 Now, at this point, its neighbor might want to have that little electron. 99 00:06:40,920 --> 00:06:47,720 So, it could get passed from that, atom into the next one, like this. 100 00:06:47,720 --> 00:06:51,810 As we start to put more atoms, or more electrons into our atoms. 101 00:06:51,810 --> 00:06:55,810 We start to see a difference in charge density and voltage. 102 00:06:55,810 --> 00:06:58,900 And this voltage leads to an electric field. 103 00:06:58,900 --> 00:07:03,540 So, as that happens, all of these atoms kind of know what's going on. 104 00:07:04,570 --> 00:07:08,530 And this field is going to cause the electrons to kind of keep moving. 105 00:07:09,600 --> 00:07:12,876 Now I call this the electron bucket brigade, because bucket brigades were a 106 00:07:12,876 --> 00:07:15,948 way of putting out fires before fire engines. 107 00:07:15,948 --> 00:07:19,328 Where people would gather buckets and they would [UNKNOWN] a big stream from a 108 00:07:19,328 --> 00:07:23,250 source of water to a fire. And they would fill up the bucket and 109 00:07:23,250 --> 00:07:26,027 kind of pass it down the chain. You don't need to wait for the first 110 00:07:26,027 --> 00:07:28,040 bucket to get all the way to the end of the chain, before passing the second 111 00:07:28,040 --> 00:07:31,270 bucket. And the same is true with electrons. 112 00:07:31,270 --> 00:07:34,520 With this electrical field, now that all of the atoms kind of know what's going 113 00:07:34,520 --> 00:07:39,010 on, these electrons can then be passed simultaneously. 114 00:07:39,010 --> 00:07:45,110 So, now all of these atoms can then just exchange the electrons at once. 115 00:07:45,110 --> 00:07:48,320 And all of this is transmitted by using this electrical field. 116 00:07:48,320 --> 00:07:51,358 And it turns out that because we don't care if the electron that we get out is 117 00:07:51,358 --> 00:07:55,692 the same as the electron we get in. That the electrons themselves could flow 118 00:07:55,692 --> 00:07:59,000 very slowly through materials. Even though the currents can be very 119 00:07:59,000 --> 00:08:00,862 large. Now we're going to actually figure out 120 00:08:00,862 --> 00:08:05,150 how to calculate a resistance based on some things that we know. 121 00:08:05,150 --> 00:08:08,615 So, the first thing we are going to need to be able to do this is some idea of how 122 00:08:08,615 --> 00:08:13,330 willing is this material to let current pass through it. 123 00:08:13,330 --> 00:08:16,498 Now you could do this by finding out, how many free electrons there are and doing 124 00:08:16,498 --> 00:08:20,952 some things like that. But to simplify all this out, we use one 125 00:08:20,952 --> 00:08:25,273 value, the resistivity. And we represent the resistivity with a 126 00:08:25,273 --> 00:08:29,300 lowercase rho, a Greek character that kind of looks like a lowercase p. 127 00:08:30,520 --> 00:08:33,160 This lets us know how willing the material is, to allow electrons to pass 128 00:08:33,160 --> 00:08:37,550 through it. When we want to calculate the resistance 129 00:08:37,550 --> 00:08:41,235 we can do so, by saying the resistance is equal to the resistivity, rho, times the 130 00:08:41,235 --> 00:08:45,140 length of the material, all divided by the area. 131 00:08:46,240 --> 00:08:48,886 And this is because it's a lot easier to, well and you can think of this kind of 132 00:08:48,886 --> 00:08:52,389 like a water analogy. It's a lot easier to get water to pass 133 00:08:52,389 --> 00:08:58,280 through a big, fat pipe that's short, than a really long pipe, that is narrow. 134 00:08:58,280 --> 00:09:02,140 And the same basically holds true with, these resistances. 135 00:09:02,140 --> 00:09:05,040 So, to calculate this, it's very simple, you just kind of plug in the numbers. 136 00:09:05,040 --> 00:09:09,460 So, I've placed the numbers here, the area is 1, square millimeter, the length 137 00:09:09,460 --> 00:09:15,160 is 50 millimeters, and the, resistivity is 10 ohm meters. 138 00:09:15,160 --> 00:09:16,400 Which is the units that we use for resistivity. 139 00:09:16,400 --> 00:09:20,360 So, I'm going to give you a second to try to calculate this yourself. 140 00:09:20,360 --> 00:09:22,615 I'm going to put up a little pause button, so you can pause the video. 141 00:09:22,615 --> 00:09:25,429 And then after you've had a chance to calculate it, then go ahead and start the 142 00:09:25,429 --> 00:09:34,030 video again and we'll check your answer. So, what did you come up with? 143 00:09:34,030 --> 00:09:36,905 Let's go through analysis, and see what we can, what result we get. 144 00:09:36,905 --> 00:09:44,010 So, the first thing we have is the equation R, is rho L, over A. 145 00:09:44,010 --> 00:09:47,325 Now you might have to calculate what the A is, for example if I had just given you 146 00:09:47,325 --> 00:09:53,410 the diameter, you might have to use. The, equation for the area of a circle. 147 00:09:53,410 --> 00:09:57,240 But I just gave you the area here. So, we can just plug in our numbers. 148 00:09:57,240 --> 00:10:05,479 I have 10 ohm meters for our resistivity. We're going to multiply that by our 149 00:10:05,479 --> 00:10:12,913 length, which is 50 millimeters and divide all of that by one square 150 00:10:12,913 --> 00:10:19,272 millimeter. So, first of all we have millimeters up 151 00:10:19,272 --> 00:10:22,420 here at the top. And millimeters down here on the bottom. 152 00:10:23,540 --> 00:10:25,980 Here we have a meter, so that cancels out with this meter. 153 00:10:27,410 --> 00:10:29,530 And so now we have a 10 to the negative 3rd on the bottom. 154 00:10:29,530 --> 00:10:34,081 So, it's the same thing as multiplying by 10 to the negative 3rd on the top. 155 00:10:34,081 --> 00:10:41,181 So, we get 10 times 10 to the 3rd, or, 10 kilo ohms as the resistance. 156 00:10:41,181 --> 00:10:43,085 So, how did you do? You get it right? 157 00:10:43,085 --> 00:10:46,117 So, fairly simple problem. and if the geometry gets a little more 158 00:10:46,117 --> 00:10:48,928 complicated, then it might be a little bit harder to solve. 159 00:10:48,928 --> 00:10:51,750 But, essentially this is all you need to do to find the resistance. 160 00:10:51,750 --> 00:10:55,525 Through a wire or any other material. To help you get a little bit better idea 161 00:10:55,525 --> 00:10:59,425 of the orders that we see when we're talking about resistance, we've included 162 00:10:59,425 --> 00:11:04,057 this little table. so conductors, things like aluminum and 163 00:11:04,057 --> 00:11:06,930 copper have resistivities on the order of 10 to the negative 8. 164 00:11:07,990 --> 00:11:11,040 so lots of free electrons, very low resistance. 165 00:11:11,040 --> 00:11:14,820 Things like silicon have a lot of variety, based on who its neighbors are 166 00:11:14,820 --> 00:11:18,950 as to what kind of resistance you see, resistivity. 167 00:11:18,950 --> 00:11:21,958 It's on the order of 10 to the negative 5th to 1 there's a lot of variety that 168 00:11:21,958 --> 00:11:26,194 you can see there. Insulators also show a lot of variety, 169 00:11:26,194 --> 00:11:29,956 even within the same piece of material different parts of the material can have 170 00:11:29,956 --> 00:11:34,680 varying resistivities. But, to give you some idea. 171 00:11:34,680 --> 00:11:37,650 We've had things on order of 10 to the 12th to 10 to the 22nd. 172 00:11:37,650 --> 00:11:41,074 Really, really, big resistivities. So, as you can see there is a, a great 173 00:11:41,074 --> 00:11:44,510 divide, between insulators that don't allow current to flow well. 174 00:11:44,510 --> 00:11:49,863 And conductors which do. In summary, we used our background 175 00:11:49,863 --> 00:11:52,824 material from the first module of this course to see how voltage and current 176 00:11:52,824 --> 00:11:55,960 relate. Through these materials. 177 00:11:55,960 --> 00:11:58,316 And then we introduce Ohm's Law, which you're going to be using frequently 178 00:11:58,316 --> 00:12:01,433 throughout the course. We'll also discuss the physical cause 179 00:12:01,433 --> 00:12:04,781 that gives us resistance as well as we calculated the resistance using the 180 00:12:04,781 --> 00:12:09,250 dimensionality and this ideas of resistivity of the material. 181 00:12:11,310 --> 00:12:14,201 So in the next lesson, we're going to look at the laws which describe the 182 00:12:14,201 --> 00:12:18,306 relationship between devices is systems. So, this was looking at single devices 183 00:12:18,306 --> 00:12:21,930 these resistive devices, now, we're going to start putting them into systems. 184 00:12:21,930 --> 00:12:24,945 And looking at some laws, that describe how all of these things interact with one 185 00:12:24,945 --> 00:12:27,209 another. If you have any questions about the 186 00:12:27,209 --> 00:12:30,577 material we covered in this class. I encourage you to go to the forums and 187 00:12:30,577 --> 00:12:33,697 post there, so that either Doctor Perry and I, or the TAs or even some of your 188 00:12:33,697 --> 00:12:37,069 fellow students. Might be able to help answer the 189 00:12:37,069 --> 00:12:40,160 questions that you might have. Until next time.