1 00:00:00 --> 00:00:00,234 2 00:00:00,234 --> 00:00:14,63 When positive charges move in unintelligible directions, 3 00:00:14,63 --> 00:00:27,98 then per definition, we say the current goes in this 4 00:00:27,98 --> 00:00:33,895 direction. When negative charges go in 5 00:00:33,895 --> 00:00:37,283 this direction, we also say the current goes in 6 00:00:37,283 --> 00:00:40,377 that direction, that's just our convention. 7 00:00:40,377 --> 00:00:44,06 If I apply a potential difference over a conductor, 8 00:00:44,06 --> 00:00:47,669 then I'm going to create an electric field in that 9 00:00:47,669 --> 00:00:50,615 conductor. And the electrons -- there are 10 00:00:50,615 --> 00:00:54,003 free electrons in a conductor -- they can move, 11 00:00:54,003 --> 00:00:57,907 but the ions cannot move, because they are frozen into 12 00:00:57,907 --> 00:01:03,195 the solid, into the crystal. And so when a current flows in 13 00:01:03,195 --> 00:01:07,152 a conductor, it's always the electrons that are responsible 14 00:01:07,152 --> 00:01:10,36 for the current. The electrons fuel the electric 15 00:01:10,36 --> 00:01:14,454 fields, and then the electrons try to make the electric field 16 00:01:14,454 --> 00:01:18,412 zero, but they can't succeed, because we keep the potential 17 00:01:18,412 --> 00:01:22,096 difference over the conductor. Often, there is a linear 18 00:01:22,096 --> 00:01:25,235 relationship between current and the potential, 19 00:01:25,235 --> 00:01:27,828 in which case, we talk about Ohm's Law. 20 00:01:27,828 --> 00:01:31,308 Now, I will try to derive Ohm's Law 21 00:01:31,308 --> 00:01:34,507 in a very crude way, a poor man's version, 22 00:01:34,507 --> 00:01:37,705 and not really one hundred percent kosher, 23 00:01:37,705 --> 00:01:42,307 it requires quantum mechanics, which is beyond the course -- 24 00:01:42,307 --> 00:01:46,987 beyond this course -- but I will do a job that still gives us 25 00:01:46,987 --> 00:01:50,029 some interesting insight into Ohm's Law. 26 00:01:50,029 --> 00:01:53,539 If I start off with a conductor, for instance, 27 00:01:53,539 --> 00:01:57,985 copper, at room temperature, three hundred degrees Kelvin, 28 00:01:57,985 --> 00:02:01,183 the free electrons in copper have a speed, 29 00:02:01,183 --> 00:02:06,903 an average speed of about a million meters per second. 30 00:02:06,903 --> 00:02:11,477 So this is the average speed of those free electrons, 31 00:02:11,477 --> 00:02:14,38 about a million meters per second. 32 00:02:14,38 --> 00:02:18,338 This in all directions. It's a chaotic motion. 33 00:02:18,338 --> 00:02:22,737 It's a thermal motion, it's due to the temperature. 34 00:02:22,737 --> 00:02:28,102 The time between collisions -- time between the collisions -- 35 00:02:28,102 --> 00:02:33,468 and this is a collision of the free electron with the atoms -- 36 00:02:33,468 --> 00:02:38,483 is approximately -- I call it tau -- 37 00:02:38,483 --> 00:02:43,885 is about three times ten to the minus fourteen seconds. 38 00:02:43,885 --> 00:02:48,188 No surprise, because the speed is enormously 39 00:02:48,188 --> 00:02:50,889 high. And the number of free 40 00:02:50,889 --> 00:02:56,592 electrons in copper per cubic meter, I call that number N, 41 00:02:56,592 --> 00:02:59,694 is about ten to the twenty-nine. 42 00:02:59,694 --> 00:03:04,296 There's about one free electron for every atom. 43 00:03:04,296 --> 00:03:10,205 So we get twen- ten to the twenty-nine free electrons per 44 00:03:10,205 --> 00:03:12,947 cubic meter. So now imagine that I apply a 45 00:03:12,947 --> 00:03:16,759 potential difference piece of copper -- or any conductor, 46 00:03:16,759 --> 00:03:20,37 for that matter -- then the electrons will experience a 47 00:03:20,37 --> 00:03:24,383 force which is the charge of the electron, that's my little E 48 00:03:24,383 --> 00:03:27,191 times the electric field that I'm creating, 49 00:03:27,191 --> 00:03:29,733 because I apply a potential difference. 50 00:03:29,733 --> 00:03:33,277 I realize that the force and the electric field are in 51 00:03:33,277 --> 00:03:36,888 opposite directions for electrons, but that's a detail, 52 00:03:36,888 --> 00:03:41,373 I'm interested in the magnitudes only. 53 00:03:41,373 --> 00:03:46,104 And so now these electrons will experience an acceleration, 54 00:03:46,104 --> 00:03:50,509 which is the force divided by the mass of the electron, 55 00:03:50,509 --> 00:03:55,078 and so they will pick up, eh, speed, between these colli- 56 00:03:55,078 --> 00:03:58,667 collisions, which we call the drift velocity, 57 00:03:58,667 --> 00:04:02,256 which is A times tau, it's just eight oh one. 58 00:04:02,256 --> 00:04:06,09 And so A equals F divided by M. E F is in the A, 59 00:04:06,09 --> 00:04:10,659 so we get E times E divided by the mass of the electrons, 60 00:04:10,659 --> 00:04:14,738 times tau. And that is the 61 00:04:14,738 --> 00:04:18,9 the drift velocity. When the electric field goes 62 00:04:18,9 --> 00:04:24,391 up, the drift velocity goes up, so the electrons move faster in 63 00:04:24,391 --> 00:04:27,667 the direction opposite to the current. 64 00:04:27,667 --> 00:04:32,45 If the time between collisions gets larger, they -- the 65 00:04:32,45 --> 00:04:37,409 acceleration lasts longer, so also, they pick up a larger 66 00:04:37,409 --> 00:04:40,686 speed, so that's intuitively pleasing. 67 00:04:40,686 --> 00:04:45,291 If we take a specific case, and I take, for instance, 68 00:04:45,291 --> 00:04:50,084 copper, and I apply over the -- over a 69 00:04:50,084 --> 00:04:56,153 wire -- let's say the wire has a length of 10 meters -- I apply a 70 00:04:56,153 --> 00:05:01,558 potential difference I call delta V, but I could have said 71 00:05:01,558 --> 00:05:06,489 just V -- I apply there a potential difference of ten 72 00:05:06,489 --> 00:05:11,61 volts, then the electric field -- inside the conductor, 73 00:05:11,61 --> 00:05:14,834 now -- is about one volt per meter. 74 00:05:14,834 --> 00:05:20,155 And so I can calculate, now, for that specific case, 75 00:05:20,155 --> 00:05:23,587 I can calculate what the drift velocity would be. 76 00:05:23,587 --> 00:05:27,663 So the drift velocity of those free electrons would be the 77 00:05:27,663 --> 00:05:31,31 charge of the electron, which is one point six times 78 00:05:31,31 --> 00:05:33,742 ten to the minus nineteen Coulombs. 79 00:05:33,742 --> 00:05:37,031 The E field is one, so I can forget about that. 80 00:05:37,031 --> 00:05:40,178 Tau is three times ten to the minus fourteen, 81 00:05:40,178 --> 00:05:43,825 as long as I'm room temperature, and the mass of the 82 00:05:43,825 --> 00:05:48,687 electron is about ten to the minus thirty kilograms. 83 00:05:48,687 --> 00:05:53,595 And so, if I didn't slip up, I found that this is five times 84 00:05:53,595 --> 00:05:58,253 ten to the minus three meters per second, which is half a 85 00:05:58,253 --> 00:06:02,578 centimeter per second. So imagine, due to the thermal 86 00:06:02,578 --> 00:06:07,402 motion, these free electrons move with a million meters per 87 00:06:07,402 --> 00:06:10,562 second. But due to this electric field, 88 00:06:10,562 --> 00:06:14,97 they only advance along the wire slowly, like a snail, 89 00:06:14,97 --> 00:06:20,709 with a speed on average of half a centimeter per second. 90 00:06:20,709 --> 00:06:25,002 And that goes very much against your and my own intuition, 91 00:06:25,002 --> 00:06:28,843 but this is the way it is. I mean, a turtle would go 92 00:06:28,843 --> 00:06:33,061 faster than these electrons. To go along a ten-meter wire 93 00:06:33,061 --> 00:06:36,45 would take half hour. Something that you never 94 00:06:36,45 --> 00:06:39,538 thought of. That it would take a half hour 95 00:06:39,538 --> 00:06:44,207 for these electrons to go along the wire if you apply potential 96 00:06:44,207 --> 00:06:47,747 difference of ten volts, copper ten meters long. 97 00:06:47,747 --> 00:06:51,588 Now, I want to massage this further, 98 00:06:51,588 --> 00:06:58 and see whether we can somehow squeeze out Ohm's Law, 99 00:06:58 --> 00:07:05,03 which is the linear relation between the potential and the 100 00:07:05,03 --> 00:07:09,84 current. So let me start off with a wire 101 00:07:09,84 --> 00:07:16,006 which has a cross-section A, and it has a length L, 102 00:07:16,006 --> 00:07:21,062 and I put a potential difference 103 00:07:21,062 --> 00:07:24,687 over the wire, plus here, and minus there, 104 00:07:24,687 --> 00:07:28,134 potential V, so I would get a current in 105 00:07:28,134 --> 00:07:31,581 this direction, that's our definition of 106 00:07:31,581 --> 00:07:34,498 current, going from plus to minus. 107 00:07:34,498 --> 00:07:38,299 The electrons, of course, are moving in this 108 00:07:38,299 --> 00:07:41,305 direction, with the drift velocity. 109 00:07:41,305 --> 00:07:45,724 And so the electric field in here, which is in this 110 00:07:45,724 --> 00:07:51,205 direction, that electric field is approximately V divided by L, 111 00:07:51,205 --> 00:07:56,331 potential difference divided by distance. 112 00:07:56,331 --> 00:08:00,84 In one second, these free electrons will move 113 00:08:00,84 --> 00:08:05,451 from left to right over a distance V D meters. 114 00:08:05,451 --> 00:08:10,369 So if I make any cross-section through this wire, 115 00:08:10,369 --> 00:08:16,619 anywhere, I can calculate how many electrons pass through that 116 00:08:16,619 --> 00:08:20,923 cross-section in one second. In one second, 117 00:08:20,923 --> 00:08:29,223 the volume that passes through here, the volume is V D times A 118 00:08:29,223 --> 00:08:33,581 but the number of free electrons per cubic meter is 119 00:08:33,581 --> 00:08:38,55 called N, so this is now the number of free electrons that 120 00:08:38,55 --> 00:08:42,473 passes, per second, through any cross-section. 121 00:08:42,473 --> 00:08:47,617 And each electron has a charge E, and so this is the current 122 00:08:47,617 --> 00:08:49,971 that will flow. The current, 123 00:08:49,971 --> 00:08:54,504 of course, is in this direction, but that's a detail. 124 00:08:54,504 --> 00:09:00,78 If I now substitute the drift velocity, which we have here, 125 00:09:00,78 --> 00:09:07,21 I substitute that in there, but then I find that the 126 00:09:07,21 --> 00:09:13,262 current -- I get a E squared, the charge squared, 127 00:09:13,262 --> 00:09:17,8 I get N, I get tau, I get downstairs, 128 00:09:17,8 --> 00:09:24,23 the mass of the electron, and then I get A times the 129 00:09:24,23 --> 00:09:28,894 electric field E. Because I have here, 130 00:09:28,894 --> 00:09:36,048 is electric field E. When you look at this here, 131 00:09:36,048 --> 00:09:43,019 that really depends only on the properties of by substance, 132 00:09:43,019 --> 00:09:48,789 for a given temperature. And we give that a name. 133 00:09:48,789 --> 00:09:54,558 We call this sigma, which is called conductivity. 134 00:09:54,558 --> 00:09:57,924 Conductivity. If I calculate, 135 00:09:57,924 --> 00:10:04,312 for copper, the conductivity, at room temperature, 136 00:10:04,312 --> 00:10:08,224 that's very easy, because I've given you what N 137 00:10:08,224 --> 00:10:12,561 is, on the blackboard there, ten to the twenty-nine, 138 00:10:12,561 --> 00:10:17,578 you know what tau is at room temperature, three times ten to 139 00:10:17,578 --> 00:10:20,384 the minus fourteen, so for copper, 140 00:10:20,384 --> 00:10:24,636 at room temperature, you will find about ten to the 141 00:10:24,636 --> 00:10:27,612 eighth. You will see more values fro 142 00:10:27,612 --> 00:10:30,418 sigma later on during this course. 143 00:10:30,418 --> 00:10:34,415 This is in SI units. I can massage this a little 144 00:10:34,415 --> 00:10:39,091 further, because E is V divided by L, 145 00:10:39,091 --> 00:10:46,248 and so I can write now that the current is that sigma times A 146 00:10:46,248 --> 00:10:52,093 times V divided by L. I can write it down a little 147 00:10:52,093 --> 00:10:55,433 bit differently, I can say V, 148 00:10:55,433 --> 00:11:01,04 therefore, equals L divided by sigma A, times I. 149 00:11:01,04 --> 00:11:07,719 And now, you're staring at Ohm's Law, whether you like it 150 00:11:07,719 --> 00:11:13,81 or not, because this is what we call 151 00:11:13,81 --> 00:11:17,332 the resistance, capital R. 152 00:11:17,332 --> 00:11:25,783 We often write down rho for one over sigma, and rho is called 153 00:11:25,783 --> 00:11:31,135 the resistivity. So either one will do. 154 00:11:31,135 --> 00:11:40,995 So you can also write down -- you can write down V equals I R, 155 00:11:40,995 --> 00:11:47,693 and this R, then, is either L divided by sigma A, 156 00:11:47,693 --> 00:11:56,065 or L times rho -- let me make it a nicer rho -- divided by A. 157 00:11:56,065 --> 00:12:03,182 That's the same thing. The units for resistance R is 158 00:12:03,182 --> 00:12:08,485 volts per ampere, but we call that ohm. 159 00:12:08,485 --> 00:12:16,858 And so the unit for R is ohm. And so if you want to know what 160 00:12:16,858 --> 00:12:20,87 the unit for rho and sigma is, 161 00:12:20,87 --> 00:12:24,273 that follows immediately from the equations. 162 00:12:24,273 --> 00:12:27,044 The unit for rho is then ohm-meters. 163 00:12:27,044 --> 00:12:31,239 So we have derived the resistance here in terms of the 164 00:12:31,239 --> 00:12:34,326 dimensions -- namely, the length and the 165 00:12:34,326 --> 00:12:38,6 cross-section -- but also in terms of the physics on an 166 00:12:38,6 --> 00:12:41,292 atomic scale, which, all by itself, 167 00:12:41,292 --> 00:12:44,854 is interesting. If you look at the resistance, 168 00:12:44,854 --> 00:12:48,89 you see it is proportional with the 169 00:12:48,89 --> 00:12:52,459 length of your wire through which you drive a current. 170 00:12:52,459 --> 00:12:55,826 Think of this as water trying to go through a pipe. 171 00:12:55,826 --> 00:12:59,26 If you make the pipe longer, the resistance goes up, 172 00:12:59,26 --> 00:13:01,617 so that's very intuitively pleasing. 173 00:13:01,617 --> 00:13:03,839 Notice that you have A downstairs. 174 00:13:03,839 --> 00:13:07,407 That means if the pipe is wider, larger cross-section, 175 00:13:07,407 --> 00:13:10,101 it's also easier for the current to flow, 176 00:13:10,101 --> 00:13:12,323 it's easier for the water to flow. 177 00:13:12,323 --> 00:13:15,42 So that's also quite pleasing. Ohm's Law, also, 178 00:13:15,42 --> 00:13:21,123 often holds for insulators, which are not conductors, 179 00:13:21,123 --> 00:13:26,229 even though I have derived it here for conductors, 180 00:13:26,229 --> 00:13:29,459 which have these free electrons. 181 00:13:29,459 --> 00:13:35,295 And so now, I want to make a comparison between very good 182 00:13:35,295 --> 00:13:39,046 conductors, and very good insulators. 183 00:13:39,046 --> 00:13:44,048 So I'll start off with a -- a chunk of material , 184 00:13:44,048 --> 00:13:52,384 cross-sectional area A -- let's take it one millimeter by one 185 00:13:52,384 --> 00:13:59,253 millimeter -- so A is ten to the minus six square meters. 186 00:13:59,253 --> 00:14:06,244 So here I have a chunk of material, and the length of that 187 00:14:06,244 --> 00:14:12,99 material L is one meter. Put a potential difference over 188 00:14:12,99 --> 00:14:16,915 there, plus here, and minus here. 189 00:14:16,915 --> 00:14:23,538 Current will start to flow in this direction, 190 00:14:23,538 --> 00:14:26,81 electrons will flow in this direction. 191 00:14:26,81 --> 00:14:31,23 The question now is, what is the resistance of this 192 00:14:31,23 --> 00:14:34,236 chunk of material? Well, very easy. 193 00:14:34,236 --> 00:14:37,95 You take these equations, you know L and A, 194 00:14:37,95 --> 00:14:42,812 so if I tell you what sigma is, then you can immediately 195 00:14:42,812 --> 00:14:45,641 calculate what the resistance is. 196 00:14:45,641 --> 00:14:49,001 So let's take, first, a good conductor. 197 00:14:49,001 --> 00:14:53,422 Silver and gold and copper are very 198 00:14:53,422 --> 00:14:57,528 good conductors. They would have values of 199 00:14:57,528 --> 00:15:02,937 sigma, ten to the eight, we just calculated for copper, 200 00:15:02,937 --> 00:15:06,643 you've seen in front of your own eyes. 201 00:15:06,643 --> 00:15:11,551 So that means rho would be ten to the minus eight, 202 00:15:11,551 --> 00:15:16,659 it's one over sigma. And so in this particular case, 203 00:15:16,659 --> 00:15:22,468 since A is ten to the minus six, the resistance R is simply 204 00:15:22,468 --> 00:15:26,498 ten to the sixth times rho. 205 00:15:26,498 --> 00:15:32,24 Because L is one meter. So it's very easy -- resistance 206 00:15:32,24 --> 00:15:36,174 here, R, is ten to the minus two ohms. 207 00:15:36,174 --> 00:15:41,702 One-hundredth of an ohm. For this material if it were 208 00:15:41,702 --> 00:15:45,211 copper. Let's now take a very good 209 00:15:45,211 --> 00:15:48,401 insulator. Glass is an example. 210 00:15:48,401 --> 00:15:52,548 Quartz, porcelain, very good insulators. 211 00:15:52,548 --> 00:15:58,571 Now, sigma, the conductivity, is extremely low. 212 00:15:58,571 --> 00:16:03,867 They vary somewhere from ten to the minus twelve through ten to 213 00:16:03,867 --> 00:16:06,429 the minus sixteen. So rho, now, 214 00:16:06,429 --> 00:16:10,187 the resistivity, is something like ten to the 215 00:16:10,187 --> 00:16:15,141 twelve to twelve to the plus sixteens, and if I take ten to 216 00:16:15,141 --> 00:16:18,899 the fourteen, just I grab -- I have to grab a 217 00:16:18,899 --> 00:16:23,939 number -- then you'll find that R, now, is ten to the twenty 218 00:16:23,939 --> 00:16:26,416 ohms. A one with twenty zeros. 219 00:16:26,416 --> 00:16:32,519 That's an enormous resistance. So you see the difference -- 220 00:16:32,519 --> 00:16:36,791 twenty-two orders of magnitude difference between a good 221 00:16:36,791 --> 00:16:41,374 conductor and a good insulator. And if I make this potential 222 00:16:41,374 --> 00:16:45,18 difference over the wire, if I make that one volt, 223 00:16:45,18 --> 00:16:48,132 and if I apply Ohm's Law, V equals I R, 224 00:16:48,132 --> 00:16:52,715 then I can also calculate the current that is going to flow. 225 00:16:52,715 --> 00:16:55,666 If I R is one, then the current here is 226 00:16:55,666 --> 00:17:00,172 hundred amperes, and the current here is ten 227 00:17:00,172 --> 00:17:07,612 to the minus twenty amperes, an insignificant current, 228 00:17:07,612 --> 00:17:11,883 ten to the minus twenty amperes. 229 00:17:11,883 --> 00:17:19,875 I first want to demonstrate to you that Ohm's Law sometimes 230 00:17:19,875 --> 00:17:24,284 holds, I will do a demonstration, 231 00:17:24,284 --> 00:17:35,169 whereby you have a voltage supply -- put a V in here -- 232 00:17:35,169 --> 00:17:40,93 and we change the voltage in a matter of a few seconds from 233 00:17:40,93 --> 00:17:45,002 zero to four volts. This is the plus side, 234 00:17:45,002 --> 00:17:50,168 this is the minus side, I have connected it here to a 235 00:17:50,168 --> 00:17:55,631 resistor which is fifty ohms -- we use this symbol for a 236 00:17:55,631 --> 00:17:59,505 resistor -- and here is a current meter. 237 00:17:59,505 --> 00:18:04,174 And the current meter has negligible resistance, 238 00:18:04,174 --> 00:18:09,81 so you can ignore that. And I'm going to show you on an 239 00:18:09,81 --> 00:18:13,334 oscilloscope -- we've never discussed an oscilloscope, 240 00:18:13,334 --> 00:18:17,057 but maybe we will in the future -- I'm going to show you, 241 00:18:17,057 --> 00:18:20,713 they are projected -- the voltage unintelligible go from 242 00:18:20,713 --> 00:18:22,841 zero to four, versus the current. 243 00:18:22,841 --> 00:18:26,497 And so it will start here, and by the time we reach four 244 00:18:26,497 --> 00:18:29,821 volts, then we would have reached a current of four 245 00:18:29,821 --> 00:18:32,48 divided by fifty, according to Ohm's Law, 246 00:18:32,48 --> 00:18:35,937 I will write down just four divided by fifty amperes, 247 00:18:35,937 --> 00:18:39,582 which is point oh eight amperes. 248 00:18:39,582 --> 00:18:44,312 And if Ohm's Law holds, then you would find a straight 249 00:18:44,312 --> 00:18:47,169 line. That's the whole idea about 250 00:18:47,169 --> 00:18:51,542 Ohm's Law, that the potential difference, linearly 251 00:18:51,542 --> 00:18:56,184 proportional to the current. You double the potential 252 00:18:56,184 --> 00:18:59,04 difference, your current doubles. 253 00:18:59,04 --> 00:19:02,878 So let's do that, let's take a look at that, 254 00:19:02,878 --> 00:19:07,876 you're going to see that there -- and I have to change my 255 00:19:07,876 --> 00:19:12,373 lights so that you get a good shot at it 256 00:19:12,373 --> 00:19:16,225 -- oh, it's already going. So you see, horizontally, 257 00:19:16,225 --> 00:19:18,868 we have the current, and vertically, 258 00:19:18,868 --> 00:19:22,644 we have the voltage. And so it takes about a second 259 00:19:22,644 --> 00:19:26,873 to go from zero to four -- so this goes from zero to four 260 00:19:26,873 --> 00:19:31,556 volts -- and you'll see that the current is beautifully linear. 261 00:19:31,556 --> 00:19:35,332 Yes, I'm blocking it -- oh, no, it's my reflection, 262 00:19:35,332 --> 00:19:38,806 that's interesting. Ohm's Law doesn't allow for 263 00:19:38,806 --> 00:19:42,76 that. So you see how beautifully 264 00:19:42,76 --> 00:19:46,314 linear it is. So now, you may have great 265 00:19:46,314 --> 00:19:51,051 confidence in Ohm's Law. Don't have any confidence in 266 00:19:51,051 --> 00:19:54,422 Ohm's Law. The conductivity sigma is a 267 00:19:54,422 --> 00:19:57,52 strong function of the temperature. 268 00:19:57,52 --> 00:20:01,984 If you increase the temperature, then the time tau 269 00:20:01,984 --> 00:20:07,451 between collisions goes down, because the speed of these free 270 00:20:07,451 --> 00:20:12,917 electrons goes up. It's a very strong function 271 00:20:12,917 --> 00:20:16,277 of temperature. And so if tau goes down, 272 00:20:16,277 --> 00:20:19,808 then clearly, what will happen is that the 273 00:20:19,808 --> 00:20:24,632 conductivity will go down. And that means rho will go up. 274 00:20:24,632 --> 00:20:29,455 And so you get more resistance. And so when you heat up a 275 00:20:29,455 --> 00:20:32,297 substance, the resistance goes up. 276 00:20:32,297 --> 00:20:35,657 A higher temperature, higher resistance. 277 00:20:35,657 --> 00:20:40,222 So the moment that the resistance R becomes a function 278 00:20:40,222 --> 00:20:42,941 of the temperature, 279 00:20:42,941 --> 00:20:46,354 I call that a total breakdown of V equals I R, 280 00:20:46,354 --> 00:20:50,602 a total breakdown of Ohm's Law. If you look in your book, 281 00:20:50,602 --> 00:20:53,484 they say, "Oh, no, no, no, that's not a 282 00:20:53,484 --> 00:20:56,594 breakdown. You just have to adjust the re- 283 00:20:56,594 --> 00:21:00,311 the resistance for a different temperature." Well, 284 00:21:00,311 --> 00:21:04,862 yes, that's an incredible poor man's way of saving a law that 285 00:21:04,862 --> 00:21:08,503 is a very bad law. Because the temperature itself 286 00:21:08,503 --> 00:21:14,217 is a function of current, the higher the current the 287 00:21:14,217 --> 00:21:18,136 higher the temperature. And so now, you get a ratio, 288 00:21:18,136 --> 00:21:21,44 V divided by I, which is no longer constant. 289 00:21:21,44 --> 00:21:24,206 It becomes a function of the current. 290 00:21:24,206 --> 00:21:28,662 That's the end of Ohm's Law. And so I want to show you that 291 00:21:28,662 --> 00:21:33,272 if I do the same experiment that I did here, but if I replace 292 00:21:33,272 --> 00:21:37,882 this by a light bulb of fifty ohms -- it's a very small light 293 00:21:37,882 --> 00:21:41,34 bulb, resistance when it is hot is fifty ohms, 294 00:21:41,34 --> 00:21:45,087 when it is cold, it is seven ohms. 295 00:21:45,087 --> 00:21:48,801 So R cold of the light bulb is roughly seven ohms, 296 00:21:48,801 --> 00:21:53,349 I believe, but I know that when it is hot, it's very close to 297 00:21:53,349 --> 00:21:56,457 the fifty ohms. Think it's a little lower. 298 00:21:56,457 --> 00:21:59,792 What do you expect now? Well, you expect now, 299 00:21:59,792 --> 00:22:03,431 that when the resistance is low in the beginning, 300 00:22:03,431 --> 00:22:06,539 you get this, and then when the resistance 301 00:22:06,539 --> 00:22:09,04 goes up, you're going to get this. 302 00:22:09,04 --> 00:22:13,285 I may end up a little higher current, because I think the 303 00:22:13,285 --> 00:22:17,702 resistance is a little lower than fifty ohms. 304 00:22:17,702 --> 00:22:21,599 And if you see a curve like this, that's not linear anymore. 305 00:22:21,599 --> 00:22:25,629 So that's the end of Ohm's Law. And that's what I want to show 306 00:22:25,629 --> 00:22:27,214 you now. So, all I do is, 307 00:22:27,214 --> 00:22:31,243 here I have this little light bulb -- for those of you who sit 308 00:22:31,243 --> 00:22:35,14 close, they can actually see that light bulb start glowing, 309 00:22:35,14 --> 00:22:38,839 but that's not important, I really want you to see that V 310 00:22:38,839 --> 00:22:41,614 versus I is no longer linear, there you go. 311 00:22:41,614 --> 00:22:44,322 And you see, every time you see this light 312 00:22:44,322 --> 00:22:50,494 bulb go on, it heats up, and during the heating up, 313 00:22:50,494 --> 00:22:54,107 it, um, the resistance increases. 314 00:22:54,107 --> 00:22:59,753 And it's the end of Ohm's Law, for this light bulb, 315 00:22:59,753 --> 00:23:03,592 at least. It was fine for the other 316 00:23:03,592 --> 00:23:09,125 resistor, but it was not fine for this light bulb. 317 00:23:09,125 --> 0. 318 0. --> 00:23:12,738 There is another way that I can That is the resistivity, 319 00:23:12,738 --> 00:23:20,755 show you that Ohm's Law is not always doing so well. 320 00:23:20,755 --> 00:23:25,568 I have a hundred twenty-five volt power supply, 321 00:23:25,568 --> 00:23:31,95 so V is hundred and twenty-five volts -- this is the potential 322 00:23:31,95 --> 00:23:37,601 difference -- and I have a light bulb, you see it here, 323 00:23:37,601 --> 00:23:43,565 that's the light bulb -- the resistance of the light bulb, 324 00:23:43,565 --> 00:23:47,332 cold, I believe, is twenty-five ohms, 325 00:23:47,332 --> 00:23:53,192 and hot, is about two hundred and fifty ohms. 326 00:23:53,192 --> 00:23:57,141 A huge difference. So if the resistance -- if I 327 00:23:57,141 --> 00:24:01,763 take the cold resistance, then I would get five amperes, 328 00:24:01,763 --> 00:24:06,89 but by the time that the bulb is hot, I would only get half an 329 00:24:06,89 --> 00:24:09,411 ampere. It's a huge difference. 330 00:24:09,411 --> 00:24:14,117 And what I want to show you, again with the oscilloscope, 331 00:24:14,117 --> 00:24:17,142 is the current as a function of time. 332 00:24:17,142 --> 00:24:23,698 When you switch on a light bulb, you would expect, 333 00:24:23,698 --> 00:24:26,879 if Ohm's Law holds, that when you switch on the 334 00:24:26,879 --> 00:24:30,753 current -- or switch on the voltage, I should say -- that 335 00:24:30,753 --> 00:24:33,797 you see this. This is then your five amperes. 336 00:24:33,797 --> 00:24:37,325 And that it would stay there. That's the whole idea. 337 00:24:37,325 --> 00:24:41,198 Namely, that the voltage divided by the current remains a 338 00:24:41,198 --> 00:24:43,827 constant. However, what you're going to 339 00:24:43,827 --> 00:24:46,11 see is like this. Current goes up, 340 00:24:46,11 --> 00:24:50,122 but then the resistance goes down, then the resistance goes 341 00:24:50,122 --> 00:24:55,356 up, when the current goes up, the resistance goes up, 342 00:24:55,356 --> 00:24:59,193 and then therefore the current will go down, 343 00:24:59,193 --> 00:25:04,279 and will level off at a level which is substantially below 344 00:25:04,279 --> 00:25:07,045 this. So you're looking there -- 345 00:25:07,045 --> 00:25:10,971 you're staring at the breakdown of Ohm's Law. 346 00:25:10,971 --> 00:25:14,629 And so that's what I want to show you now. 347 00:25:14,629 --> 00:25:19,983 So, here we need a hundred and twenty five volts -- and there 348 00:25:19,983 --> 00:25:25,516 is the light bulb, and when I throw this switch, 349 00:25:25,516 --> 00:25:29,414 you will see the pattern of the current versus time -- you will 350 00:25:29,414 --> 00:25:32,37 only see it once, and then we freeze it with the 351 00:25:32,37 --> 00:25:35,388 oscilloscope -- turn this off -- so look closely, 352 00:25:35,388 --> 00:25:36,394 now. There it is. 353 00:25:36,394 --> 00:25:39,224 Forget these little ripple that you see on it, 354 00:25:39,224 --> 00:25:42,746 it has to do with the way that we produce the hundred and 355 00:25:42,746 --> 00:25:45,135 twenty five volts. And so you see here, 356 00:25:45,135 --> 00:25:47,588 horizontally, time, the time between two 357 00:25:47,588 --> 00:25:50,48 adjacent vertical lines is twenty milliseconds. 358 00:25:50,48 --> 00:25:52,304 And so, indeed, very early on, 359 00:25:52,304 --> 00:25:56,769 the current surged toward -- to a very high value, 360 00:25:56,769 --> 00:26:01,939 and then the filament heats up, and so the resistance goes up, 361 00:26:01,939 --> 00:26:05,754 the light bulb, and the current just goes back 362 00:26:05,754 --> 00:26:08,636 again. From the far left to the far 363 00:26:08,636 --> 00:26:13,128 right on the screen is about two hundred milliseconds. 364 00:26:13,128 --> 00:26:16,095 That's about two tenths of a second. 365 00:26:16,095 --> 00:26:20,757 And here you get a current level which is way lower than 366 00:26:20,757 --> 00:26:24,656 what you get there. That's a breakdown of Ohm's 367 00:26:24,656 --> 00:26:27,453 Law. It is actually very nice that 368 00:26:27,453 --> 00:26:31,777 resistances go up with light bulbs 369 00:26:31,777 --> 00:26:34,982 when the temperature goes up. Because, suppose it were the 370 00:26:34,982 --> 00:26:37,456 other way around. Suppose you turn on a light 371 00:26:37,456 --> 00:26:39,593 bulb, and the resistance would go down. 372 00:26:39,593 --> 00:26:41,843 Light bulb got hot, resistance goes down, 373 00:26:41,843 --> 00:26:44,486 that means the current goes up. Instead of down, 374 00:26:44,486 --> 00:26:47,073 the current goes up. That means it gets hotter. 375 00:26:47,073 --> 00:26:49,772 That means the resistance goes even further down. 376 00:26:49,772 --> 00:26:52,19 That means the current goes even further up. 377 00:26:52,19 --> 00:26:55,395 And so what it would mean is that every time you turn on a 378 00:26:55,395 --> 00:26:58,151 light bulb, it would, right in front of your eyes, 379 00:26:58,151 --> 00:27:00,232 destruct itself. That's not happening. 380 00:27:00,232 --> 00:27:03,775 It's the other way around. So, in a way, 381 00:27:03,775 --> 00:27:09,027 it's fortunate that the resistance goes up when the 382 00:27:09,027 --> 00:27:12,179 light bulbs get hot. All right. 383 00:27:12,179 --> 00:27:18,692 Let's now be a little bit more qualitative on some networks of 384 00:27:18,692 --> 00:27:24,68 resistors, and we'll have you do a few problems like that, 385 00:27:24,68 --> 00:27:30,774 whereby we just will assume, naively, that Ohm's Law holds. 386 00:27:30,774 --> 00:27:37,092 In other words, we will always assume that the 387 00:27:37,092 --> 00:27:42,701 values for the resistances that we give you will not change. 388 00:27:42,701 --> 00:27:48,594 So we will assume that the heat that is produced will not play 389 00:27:48,594 --> 00:27:53,252 any important role. So we will just use Ohm's Law, 390 00:27:53,252 --> 00:27:58,67 for now, and if you can't use it, we will be very specific 391 00:27:58,67 --> 00:28:01,902 about that. So suppose I have here, 392 00:28:01,902 --> 00:28:07,32 between point A and point B, suppose I have two resistors, 393 00:28:07,32 --> 00:28:13,349 R one and R two. And suppose I apply a potential 394 00:28:13,349 --> 00:28:16,995 difference between A and B, that this be plus, 395 00:28:16,995 --> 00:28:20,965 and this be minus, and the potential difference is 396 00:28:20,965 --> 00:28:22,343 V. And you know V, 397 00:28:22,343 --> 00:28:24,53 this is known, I give you V, 398 00:28:24,53 --> 00:28:28,663 I gave you this resistance, and I gave you that one. 399 00:28:28,663 --> 00:28:32,714 So I could ask you now, what is the current that is 400 00:28:32,714 --> 00:28:35,55 going to flow? I could also ask you, 401 00:28:35,55 --> 00:28:40,087 then, what is the potential difference over this resistor 402 00:28:40,087 --> 00:28:44,994 alone -- which I will call V one -- and 403 00:28:44,994 --> 00:28:50,315 what is the potential difference over the second resistor, 404 00:28:50,315 --> 00:28:54,89 which I call V two? Very straightforward question. 405 00:28:54,89 --> 00:28:57,783 Well, you apply, now, Ohm's Law, 406 00:28:57,783 --> 00:29:02,171 and so between A and B, there are two resistors, 407 00:29:02,171 --> 00:29:05,345 in series. So the current has to go 408 00:29:05,345 --> 00:29:09,453 through both, and so the potential difference 409 00:29:09,453 --> 00:29:13,747 V, in Ohm's Law, is now the total current times 410 00:29:13,747 --> 00:29:18,714 R one plus R two. Suppose these two resistors 411 00:29:18,714 --> 00:29:21,44 were the same, they had the same length, 412 00:29:21,44 --> 00:29:25,005 same cross-sectional area. If you put two in series, 413 00:29:25,005 --> 00:29:28,709 you have twice the length. Well, so, twice the length, 414 00:29:28,709 --> 00:29:32,413 remember, resistance is linearly proportional with the 415 00:29:32,413 --> 00:29:35,208 length of a wire, and so you add them up. 416 00:29:35,208 --> 00:29:38,843 So now you know R one and you know R two, you know V, 417 00:29:38,843 --> 00:29:41,918 so you already know the current, very simple. 418 00:29:41,918 --> 00:29:45,342 You can also apply Ohm's Law, as long as it holds, 419 00:29:45,342 --> 00:29:50,637 for this resistor alone. So then you get that V one 420 00:29:50,637 --> 00:29:54,992 equals I times R one, so now you have the voltage 421 00:29:54,992 --> 00:29:57,986 over this resistor, and of course, 422 00:29:57,986 --> 00:30:01,525 V two must be the current I times R two. 423 00:30:01,525 --> 00:30:04,7 And so you have solved your problem. 424 00:30:04,7 --> 00:30:10,144 All the questions that I asked you, you have the answers to. 425 00:30:10,144 --> 00:30:14,318 We could now have a slightly different problem, 426 00:30:14,318 --> 00:30:18,855 whereby point A is here, but now we have a resistor 427 00:30:18,855 --> 00:30:22,73 here, which is R one, 428 00:30:22,73 --> 00:30:24,777 and we have here, R two. 429 00:30:24,777 --> 00:30:27,803 This is point B, and this is R two. 430 00:30:27,803 --> 00:30:32,163 And the potential difference is V, that is, again, 431 00:30:32,163 --> 00:30:37,592 given, and now I could ask you, what, now, is the current that 432 00:30:37,592 --> 00:30:41,419 will flow here? And then I can also ask you, 433 00:30:41,419 --> 00:30:46,847 what is the current that would go through one -- resistor one, 434 00:30:46,847 --> 00:30:52,097 and what is the current that could go through 435 00:30:52,097 --> 00:30:56,721 resistor two? And I would allow you to use 436 00:30:56,721 --> 00:30:59,541 Ohm's Law. So now you say, 437 00:30:59,541 --> 00:31:03,601 "Aha! The potential difference from A 438 00:31:03,601 --> 00:31:09,014 to B going this route, that potential difference, 439 00:31:09,014 --> 00:31:15,443 is V, that's a given." So V must now be I one times R one. 440 00:31:15,443 --> 00:31:19,841 That's Ohm's Law, for this upper branch. 441 00:31:19,841 --> 00:31:24,352 But, of course, you can also go the lower 442 00:31:24,352 --> 00:31:29,505 branch. So the same V is also I two 443 00:31:29,505 --> 00:31:33,561 times R two. But whatever current comes in 444 00:31:33,561 --> 00:31:39,299 here must split up between these two, think of it as water. 445 00:31:39,299 --> 00:31:44,74 You cannot get rid of charges. The number of charges per 446 00:31:44,74 --> 00:31:49,39 second that flow into this juncture continue on, 447 00:31:49,39 --> 00:31:54,139 and so I, the total current, is I one plus I two. 448 00:31:54,139 --> 00:31:58,324 And so now, you see, you have all the 449 00:31:58,324 --> 00:32:02,754 ingredients that you need to solve for the current I -- for 450 00:32:02,754 --> 00:32:06,115 the current I one, and for the current I two. 451 00:32:06,115 --> 00:32:10,774 And you can turn this into an industry, you can make extremely 452 00:32:10,774 --> 00:32:14,898 complicated networks of resistors -- and if you were in 453 00:32:14,898 --> 00:32:19,175 course six, you should love it -- I don't like it at all, 454 00:32:19,175 --> 00:32:23,376 so you don't have to worry about it, you're not going to 455 00:32:23,376 --> 00:32:27,73 get very complicated resistor net- networks 456 00:32:27,73 --> 00:32:33,772 from me -- but in course six, you're going to see a lot of 457 00:32:33,772 --> 00:32:37,482 them. They're going to throw them -- 458 00:32:37,482 --> 00:32:43,63 stuff them down your throat. The conductivity of a substan- 459 00:32:43,63 --> 00:32:49,461 substance goes up if I can increase the number of charge 460 00:32:49,461 --> 00:32:52,535 carriers. If we have dry air, 461 00:32:52,535 --> 00:32:57,199 and it is cold, then the resistivity of cold, 462 00:32:57,199 --> 00:33:04,247 dry air at one atmosphere -- so rho for 463 00:33:04,247 --> 00:33:10,323 air, cold, dry, one atmosphere -- cold means 464 00:33:10,323 --> 00:33:19,024 temperature that we have outside -- it's about four times ten to 465 00:33:19,024 --> 00:33:25,101 the thirteen. That is the resistivity of air. 466 00:33:25,101 --> 00:33:34,888 It is about what it is in this room, maybe a little 467 00:33:34,888 --> 00:33:38,912 lower, because the temperature is a little higher. 468 00:33:38,912 --> 00:33:43,675 If I heat it up -- the air -- then the conductivity will go 469 00:33:43,675 --> 00:33:45,975 up. Resistivity will go down, 470 00:33:45,975 --> 00:33:49,259 because now, I create oxygen and nitrogen 471 00:33:49,259 --> 00:33:53,53 ions by heating up the air. Remember when we had this 472 00:33:53,53 --> 00:33:58,128 lightning, the unintelligible came down, and we created a 473 00:33:58,128 --> 00:34:04,451 channel full of ions and electrons, that had a very low 474 00:34:04,451 --> 00:34:07,732 resistivity, a very high conductivity. 475 00:34:07,732 --> 00:34:11,278 And so what I want to demonstrate to you, 476 00:34:11,278 --> 00:34:16,686 that when I create ions in this room, that I can actually make 477 00:34:16,686 --> 00:34:20,409 the conductivity of air go up tremendously. 478 00:34:20,409 --> 00:34:24,931 Not only will the electrons move, but also the ions, 479 00:34:24,931 --> 00:34:29,452 now, will start to move. And the way I'm going to do 480 00:34:29,452 --> 00:34:34,594 that is, I'm going to put charge on the electroscope -- oh, 481 00:34:34,594 --> 00:34:39,388 that is not so good -- no harm done. 482 00:34:39,388 --> 00:34:44,393 I'm going to put charge on the electroscope, 483 00:34:44,393 --> 00:34:50,795 and you will see that the conductivity of air is so poor 484 00:34:50,795 --> 00:34:54,637 that it will stay there for hours. 485 00:34:54,637 --> 00:35:00,341 And then what I will do, I will create ions in the 486 00:35:00,341 --> 00:35:07,325 vicinity of the electroscope. But let's first put some charge 487 00:35:07,325 --> 00:35:15,24 on the electroscope. I have here a glass rod and 488 00:35:15,24 --> 00:35:20,929 I'll put some charge on it. OK, that's a lot of charge. 489 00:35:20,929 --> 00:35:27,039 And, uh, the r- the air is quite dry, conductivity is very, 490 00:35:27,039 --> 00:35:33,465 very small, and so the charge cannot go off through the air to 491 00:35:33,465 --> 00:35:36,626 the surroundings, to the earth. 492 00:35:36,626 --> 00:35:42,42 But now I'm going to create ions there by heating it up, 493 00:35:42,42 --> 00:35:49,059 and I decided to do that with a candle, because a candle is 494 00:35:49,059 --> 00:35:51,437 very romantic, as we all know. 495 00:35:51,437 --> 00:35:56,111 So here I have this candle -- look how well the charge is 496 00:35:56,111 --> 00:35:59,063 holding, eh? -- and here's my candle. 497 00:35:59,063 --> 00:36:03,82 And I will bring the candle -- oh, maybe twenty centimeters 498 00:36:03,82 --> 00:36:07,51 from the electroscope. Look at it, look at it, 499 00:36:07,51 --> 00:36:11,118 already going. It's about fifteen centimeters 500 00:36:11,118 --> 00:36:13,578 away. I'll take my candle away, 501 00:36:13,578 --> 00:36:19,506 and it stops again. So it's all due to the fact 502 00:36:19,506 --> 00:36:25,302 that I'm ionizing the air there, creating free electrons as well 503 00:36:25,302 --> 00:36:30,178 as ions, and they both participate now in the current, 504 00:36:30,178 --> 00:36:35,422 and the charge can flow away from the electroscope through 505 00:36:35,422 --> 00:36:39,929 the earth, because the conductivity now is so much 506 00:36:39,929 --> 00:36:41,769 higher. I stop again, 507 00:36:41,769 --> 00:36:45,633 and it stops. You see in front of your eyes 508 00:36:45,633 --> 00:36:49,865 how important the temperature is, in this case, 509 00:36:49,865 --> 00:36:54,648 the presence of the ions in the air. 510 00:36:54,648 --> 00:36:58,087 If I have clean, distilled water -- I mean, 511 00:36:58,087 --> 00:37:01,608 clean water. I don't mean the stuff that you 512 00:37:01,608 --> 00:37:05,456 get in Cambridge, let alone did I mean the stuff 513 00:37:05,456 --> 00:37:09,386 that is in the Charles River, I mean clean water, 514 00:37:09,386 --> 00:37:13,562 that has a pH of seven. That means one out of ten to 515 00:37:13,562 --> 00:37:18,311 the seven of the water molecules is ionized, H plus and O H 516 00:37:18,311 --> 00:37:20,194 minus. The conductivity, 517 00:37:20,194 --> 00:37:24,369 by the way, is not the result of the 518 00:37:24,369 --> 00:37:27,686 free electrons, but is really the result of 519 00:37:27,686 --> 00:37:32,503 these H plus and O H minus ions. It's one of the cases whereby 520 00:37:32,503 --> 00:37:37,004 not the -- the electrons are maj- the major responsibility 521 00:37:37,004 --> 00:37:40,637 for the current. If I have add three percent of 522 00:37:40,637 --> 00:37:45,059 salt, in terms of weight, then all that salt will ionize, 523 00:37:45,059 --> 00:37:49,639 so you get sodium plus and C L minus ions, you increase the 524 00:37:49,639 --> 00:37:52,482 number of ions by an enormous factor. 525 00:37:52,482 --> 00:37:56,51 And so the conductivity will soar up 526 00:37:56,51 --> 00:38:01,609 by a factor of three hundred thousand, or up to a million, 527 00:38:01,609 --> 00:38:05,545 because you increase the ions by that amount. 528 00:38:05,545 --> 00:38:10,824 And so it's no surprise then, for you, that the conductivity 529 00:38:10,824 --> 00:38:15,744 of seawater is a million times higher -- think about it, 530 00:38:15,744 --> 00:38:21,023 a million times higher -- than the conductivity of distilled 531 00:38:21,023 --> 00:38:24,065 water. And I would like to give you 532 00:38:24,065 --> 00:38:31,625 the number for water -- so this is distilled water -- 533 00:38:31,625 --> 00:38:39,002 that is about two times ten to the fifth ohm-meters. 534 00:38:39,002 --> 0. 535 0. --> 00:38:42,619 There is another way that I can That is the resistivity, 536 00:38:42,619 --> 00:38:47,682 two times ten to the five oh-meters. 537 00:38:47,682 --> 00:38:53,468 I have here, a bucket of distilled water. 538 00:38:53,468 --> 00:39:04,461 I'll make a drawing for you on the blackboard there. 539 00:39:04,461 --> 00:39:09,643 So here is a bucket of distilled water, 540 00:39:09,643 --> 00:39:13,871 and in there, is a copper plate, 541 00:39:13,871 --> 00:39:20,689 and another copper plate, and here is a light bulb, 542 00:39:20,689 --> 00:39:27,643 and this will go straight to the outlet [wssshhht], 543 00:39:27,643 --> 00:39:34,052 stick it in, hundred ten volts. 544 00:39:34,052 --> 00:39:38,48 This light bulb has eight hundred ohm resistance when it 545 00:39:38,48 --> 00:39:41,298 is hot. You see the light bulb here. 546 00:39:41,298 --> 00:39:45,806 You can calculate what this resistance is between the two 547 00:39:45,806 --> 00:39:49,589 plates, that's easy, you have all the tools now. 548 00:39:49,589 --> 00:39:54,017 If you know the distance, it's about twenty centimeters, 549 00:39:54,017 --> 00:39:57,479 and you know the surface area of the plates, 550 00:39:57,479 --> 00:40:01,021 because remember, the resistance is inversely 551 00:40:01,021 --> 00:40:06,253 proportional with A, so you have to take that into 552 00:40:06,253 --> 00:40:09,914 account -- and you take the resistivity of water into 553 00:40:09,914 --> 00:40:13,646 account, it's a trivial calculation, you can calculate 554 00:40:13,646 --> 00:40:16,673 what the resistance is of this portion here. 555 00:40:16,673 --> 00:40:20,123 And I found that this resistance here is about two 556 00:40:20,123 --> 00:40:21,953 megaohms. Two million ohms. 557 00:40:21,953 --> 00:40:26,107 So, when I plug this into a wall, the current that will flow 558 00:40:26,107 --> 00:40:29,275 is extremely low, because it has to go through 559 00:40:29,275 --> 00:40:32,936 the eight hundred ohms, and through the two megaohms. 560 00:40:32,936 --> 00:40:36,738 So you won't see anything, the light bulb will not show 561 00:40:36,738 --> 00:40:38,765 any light. 562 00:40:38,765 --> 00:40:43,47 But now, if I -- put salt in here, if I really manage to put 563 00:40:43,47 --> 00:40:48,494 three percent in weight salt in here, then this two megaohm will 564 00:40:48,494 --> 00:40:51,763 go down to two ohms, a million times less. 565 00:40:51,763 --> 00:40:56,627 So now, the light bulb will be happy like a clam at high tide, 566 00:40:56,627 --> 00:41:00,216 because two ohms here, plus the eight hundred, 567 00:41:00,216 --> 00:41:04,522 the two is insignificant. And this is what I want to -- 568 00:41:04,522 --> 00:41:08,03 to demonstrate to you now, the 569 00:41:08,03 --> 00:41:11,965 enormous importance of increasing ions. 570 00:41:11,965 --> 00:41:16,108 I increased ions here by heating the air, 571 00:41:16,108 --> 00:41:21,182 now I'm going to increase the ions by adding salt. 572 00:41:21,182 --> 00:41:27,498 And so the first thing that I will do is, I will stick this in 573 00:41:27,498 --> 00:41:30,398 here. There's the light bulb. 574 00:41:30,398 --> 00:41:36,197 And I make a daring prediction that you will see nothing. 575 00:41:36,197 --> 00:41:38,268 There we go. Nothing. 576 00:41:38,268 --> 00:41:44,531 Isn't that amazing? You didn't expect that, 577 00:41:44,531 --> 00:41:46,916 right? Physics works. 578 00:41:46,916 --> 00:41:51,806 You see nothing. If I take the plates out, 579 00:41:51,806 --> 00:41:57,53 and touch them with each other, what will happen? 580 00:41:57,53 --> 00:42:02,658 There you go. But this water has such a huge 581 00:42:02,658 --> 00:42:07,189 resistance that the current is too low. 582 00:42:07,189 --> 00:42:14,822 Well, let's add some -- not pepper -- add some salt. 583 00:42:14,822 --> 00:42:19,823 Yes, there's salt in there. It's about as much as I would 584 00:42:19,823 --> 00:42:24,467 put on my eggs in the morning -- stir a little -- ah, 585 00:42:24,467 --> 00:42:27,771 hey, look at that. Isn't that amazing? 586 00:42:27,771 --> 00:42:32,861 And when I bring them closer together, it will become even 587 00:42:32,861 --> 00:42:37,327 brighter, because L is now smaller, the distance is 588 00:42:37,327 --> 00:42:40,452 smaller. I bring them farther apart, 589 00:42:40,452 --> 00:42:42,774 it's amazing. Just a teeny, 590 00:42:42,774 --> 00:42:48,551 weeny little bit of salt, about as much as I use on my 591 00:42:48,551 --> 00:42:53,353 egg, let alone -- what the hell, let's put everything in there 592 00:42:53,353 --> 00:42:57,21 -- that's a unintelligible I put everything, then, 593 00:42:57,21 --> 00:43:00,752 of course, you go almost down to the two ohms, 594 00:43:00,752 --> 00:43:04,531 and the light bulb will be just burning normally. 595 00:43:04,531 --> 00:43:08,782 But even with that little bit of salt, you saw the huge 596 00:43:08,782 --> 00:43:11,537 difference. My body is a fairly good 597 00:43:11,537 --> 00:43:15,63 conductor -- yours too, we all came out of the sea -- 598 00:43:15,63 --> 00:43:20,764 so we are almost all water -- and therefore, 599 00:43:20,764 --> 00:43:24,735 when we do experiments with little charge, 600 00:43:24,735 --> 00:43:28,416 like the van der Graf, being a student, 601 00:43:28,416 --> 00:43:33,161 then we have to insulate ourselves very carefully, 602 00:43:33,161 --> 00:43:37,81 putting glass plates under us, or plastic stools, 603 00:43:37,81 --> 00:43:42,556 to prevent that the charge runs down to the earth. 604 00:43:42,556 --> 00:43:47,689 In fact, the resistance, my resistance between my body 605 00:43:47,689 --> 00:43:52,629 and the earth is largely dictated by the soles of my 606 00:43:52,629 --> 00:43:56,113 shoe, not by my body, 607 00:43:56,113 --> 00:44:00,272 not by my skin. But if you look at my soles, 608 00:44:00,272 --> 00:44:05,398 then you get something like this, and it has a certain 609 00:44:05,398 --> 00:44:09,363 thickness, and this, maybe one centimeter. 610 00:44:09,363 --> 00:44:14,392 This, now, is L in my calculation for the resistance, 611 00:44:14,392 --> 00:44:18,454 because current may flow in this direction, 612 00:44:18,454 --> 00:44:22,226 so that's L. Well, how large is my foot? 613 00:44:22,226 --> 00:44:29,298 Let's say it's one foot long -- no pun implied -- and let's say 614 00:44:29,298 --> 00:44:34,649 it's about ten centimeters wide. So you can calculate what the 615 00:44:34,649 --> 00:44:37,895 surface area A is, you know what L is, 616 00:44:37,895 --> 00:44:42,018 and if you know, now what the resistivity is for 617 00:44:42,018 --> 00:44:47,194 my sole, I can make a rough guess, I looked up the material, 618 00:44:47,194 --> 00:44:51,668 and I found that the resistivity is about ten to the 619 00:44:51,668 --> 00:44:56,054 tenth. So I can now calculate what the 620 00:44:56,054 --> 00:44:58,41 resistance is in this direction. 621 00:44:58,41 --> 00:45:01,221 And I found that that resistance then, 622 00:45:01,221 --> 00:45:04,868 putting in the numbers, is about ten billion ohm. 623 00:45:04,868 --> 00:45:07,755 And you will say, "Wow!" Oh, it's four, 624 00:45:07,755 --> 00:45:09,579 actually. Well, big deal. 625 00:45:09,579 --> 00:45:12,086 Four billion ohm. So you will say, 626 00:45:12,086 --> 00:45:15,733 "That's enormous resistance!" Well, first of all, 627 00:45:15,733 --> 00:45:19,684 I'm walking on two feet, not on one, so if I would be 628 00:45:19,684 --> 00:45:23,939 standing one the whole lecture, it would probably be four 629 00:45:23,939 --> 00:45:28,878 billion, but if I have two feet on the ground, 630 00:45:28,878 --> 00:45:31,37 it's really two billion, you will say, 631 00:45:31,37 --> 00:45:34,2 "Well, that's still extremely large!" Well, 632 00:45:34,2 --> 00:45:36,76 it may look large, but it really isn't, 633 00:45:36,76 --> 00:45:40,735 because all the experiments that we are doing here in twenty 634 00:45:40,735 --> 00:45:43,834 six one hundred, you're dealing with very small 635 00:45:43,834 --> 00:45:46,934 amounts of charge. Even if you take the van der 636 00:45:46,934 --> 00:45:50,706 Graff -- the van der Graff, say, has two hundred thousand 637 00:45:50,706 --> 00:45:54,749 volts -- and let's assume that my resistance is two times ten 638 00:45:54,749 --> 00:45:57,444 to the nine ohms, two feet on the ground. 639 00:45:57,444 --> 00:46:01,014 So when I touch the van der Graff, 640 00:46:01,014 --> 00:46:04,587 the current that would flow, according to Ohm's Law, 641 00:46:04,587 --> 00:46:08,509 would be hundred microamperes. That means, in one second, 642 00:46:08,509 --> 00:46:11,732 I can take hundred microCoulombs of the van der 643 00:46:11,732 --> 00:46:16,004 Graff, but the van der Graff has only ten microCoulombs on in. 644 00:46:16,004 --> 00:46:19,857 So the resistance of four billion or two billion ohms is 645 00:46:19,857 --> 00:46:23,359 way too low for these experiments that we have been 646 00:46:23,359 --> 00:46:27,492 doing in twenty six one hundred, and that's why we use these 647 00:46:27,492 --> 00:46:30,574 plastic stools, and we use these glass plates 648 00:46:30,574 --> 00:46:34,427 in order to make sure that the current 649 00:46:34,427 --> 00:46:39,683 is not draining off the the charge that we need for the 650 00:46:39,683 --> 00:46:43,602 experiments. I want to demonstrate that to 651 00:46:43,602 --> 00:46:48,094 you, that, indeed, even with my shoes on -- that 652 00:46:48,094 --> 00:46:54,019 means, even with my two billion ohm resistance to the ground -- 653 00:46:54,019 --> 00:46:58,894 that it will be very difficult for me, for instance, 654 00:46:58,894 --> 00:47:02,048 to keep charge on an electroscope. 655 00:47:02,048 --> 00:47:07,591 I'm going to put charge on this electroscope by scuffing my 656 00:47:07,591 --> 00:47:12,617 feet. But, since I keep my -- I have 657 00:47:12,617 --> 00:47:16,529 my shoes on, I'm not standing on the glass plate, 658 00:47:16,529 --> 00:47:19,056 the charge will flow through me. 659 00:47:19,056 --> 00:47:23,376 You can apply Ohm's Law. And you will see that as I do 660 00:47:23,376 --> 00:47:28,267 this -- I'm scuffing my feet now -- that I can only keep that 661 00:47:28,267 --> 00:47:32,098 electroscope charged as long as I keep scuffing. 662 00:47:32,098 --> 00:47:35,848 But the moment that I stop scuffing, it's gone. 663 00:47:35,848 --> 00:47:38,538 Start scuffing again, that's fine, 664 00:47:38,538 --> 00:47:42,699 but the moment that I stop scuffing, 665 00:47:42,699 --> 00:47:46,627 it goes off again. Even though this resistance is 666 00:47:46,627 --> 00:47:51,537 something like two billion ohms. Let alone if I take my shoes 667 00:47:51,537 --> 00:47:53,582 off. I apologize for that. 668 00:47:53,582 --> 00:47:57,265 If now I scuff, I can't even get any charge on 669 00:47:57,265 --> 00:47:59,638 the electroscope, because now, 670 00:47:59,638 --> 00:48:02,665 the resistance is so ridiculously low, 671 00:48:02,665 --> 00:48:05,775 I don't even have the two billion ohms, 672 00:48:05,775 --> 00:48:09,621 I can't even put any charge on the electroscope. 673 00:48:09,621 --> 00:48:14,039 It's always very difficult for us to 674 00:48:14,039 --> 00:48:19,569 do these experiments unless we insulate ourselves very well. 675 00:48:19,569 --> 00:48:23,786 And if, somehow, the weather is a little damp, 676 00:48:23,786 --> 00:48:28,097 we can very thin films of water onto our tools, 677 00:48:28,097 --> 00:48:33,813 and then the current can flow off just through these very thin 678 00:48:33,813 --> 00:48:38,218 layers of water. That's why we always like to do 679 00:48:38,218 --> 00:48:43,747 these experiments in winter, so that the conductivity of the 680 00:48:43,747 --> 00:48:46,933 air is very low, no water anywhere. 681 00:48:46,933 --> 00:48:51,525 Here you see a slide of a robbery. 682 00:48:51,525 --> 00:48:57,064 I have scuffed my feet across the rug, and I am armed with a 683 00:48:57,064 --> 00:49:00,725 static charge. Hand over all your money, 684 00:49:00,725 --> 00:49:05,701 or I'll touch your nose. This person either never took 685 00:49:05,701 --> 00:49:08,987 eight oh two, or he is wearing very, 686 00:49:08,987 --> 49:14 very special shoes. See you on Wednesday.