1 00:00:00 --> 00:00:00,424 2 00:00:00,424 --> 00:00:04,332 We have often talked about power supplies, 3 00:00:04,332 --> 00:00:09,288 which are devices which maintain a constant potential 4 00:00:09,288 --> 00:00:12,815 difference. Here, we have such a power 5 00:00:12,815 --> 00:00:17,867 supply, potential difference V, this be the plus side, 6 00:00:17,867 --> 00:00:22,92 and this be the minus side. I'm going to connect this, 7 00:00:22,92 --> 00:00:27,686 I have a resistor here, R, and as a result of this, 8 00:00:27,686 --> 00:00:31,88 current will start to flow in this direction, 9 00:00:31,88 --> 00:00:35,892 this direction, this direction, 10 00:00:35,892 --> 00:00:39,579 so in the power supply, the current flows in this 11 00:00:39,579 --> 00:00:42,19 directions. Through the resistance, 12 00:00:42,19 --> 00:00:44,879 the current flows in this direction. 13 00:00:44,879 --> 00:00:47,875 In what direction is the electric field? 14 00:00:47,875 --> 00:00:52,407 The electric field always runs from plus to minus potential. 15 00:00:52,407 --> 00:00:54,788 So right here, in this resistor, 16 00:00:54,788 --> 00:00:59,32 the electric field is in this direction, from plus to minus. 17 00:00:59,32 --> 00:01:04,927 But inside the supply it must also go from plus to minus. 18 00:01:04,927 --> 00:01:09,677 And so inside the supply, the electric field is in the 19 00:01:09,677 --> 00:01:12,724 direction that opposes the current. 20 00:01:12,724 --> 00:01:17,563 So some kind of a pump mechanism must force the current 21 00:01:17,563 --> 00:01:22,133 to go inside the supply, against the electric field. 22 00:01:22,133 --> 00:01:25,09 A boulder does not, all by itself, 23 00:01:25,09 --> 00:01:29,033 move up a hill. And so something is needed to 24 00:01:29,033 --> 00:01:30,915 push it. You remember, 25 00:01:30,915 --> 00:01:36,117 with the VandeGraaff, we were spraying charge onto a 26 00:01:36,117 --> 00:01:39,938 belt, and then we rotated the belt, and the belt forces the 27 00:01:39,938 --> 00:01:42,77 charge into the dome. It had to overcome the 28 00:01:42,77 --> 00:01:46,13 repelling force of the dome. So work had to be done. 29 00:01:46,13 --> 00:01:48,634 So the energy must come from somewhere. 30 00:01:48,634 --> 00:01:52,125 And in the case of the VandeGraaff, it was clearly the 31 00:01:52,125 --> 00:01:54,233 motor that kept the belt running. 32 00:01:54,233 --> 00:01:58,054 In the case of the Wimshurst it was I who turned the crank, 33 00:01:58,054 --> 00:02:00,36 so I did work. In the case of common 34 00:02:00,36 --> 00:02:03,324 batteries, the ones that you buy in the store, 35 00:02:03,324 --> 00:02:06,947 it is chemical energy that provides 36 00:02:06,947 --> 00:02:12,201 the energy. And I will discuss now with you 37 00:02:12,201 --> 00:02:18,705 and demonstrate a particular kind of chemical energy, 38 00:02:18,705 --> 00:02:25,959 which is one whereby we have a zinc and a copper plate in a 39 00:02:25,959 --> 00:02:29,086 solution. So we have here, 40 00:02:29,086 --> 00:02:32,713 H two S O 4, and we have here, 41 00:02:32,713 --> 00:02:39,592 zinc plate, and we have here a copper plate. 42 00:02:39,592 --> 00:02:44,228 This side will become positive, and this side will become 43 00:02:44,228 --> 00:02:46,96 negative. You will get a potential 44 00:02:46,96 --> 00:02:49,858 difference between these two plates. 45 00:02:49,858 --> 00:02:53,914 To understand that really takes quantum mechanics, 46 00:02:53,914 --> 00:02:58,633 this goes beyond this course. But the potential difference 47 00:02:58,633 --> 00:03:02,772 that you get is normally something around one volt. 48 00:03:02,772 --> 00:03:06,415 The secret, really, is not necessarily in the 49 00:03:06,415 --> 00:03:10,389 solution, because if you take two 50 00:03:10,389 --> 00:03:15,491 conductors, two different conductors, and you touch them, 51 00:03:15,491 --> 00:03:19,591 metal on metal, there will also be a potential 52 00:03:19,591 --> 00:03:23,053 difference. So let's look at his now in 53 00:03:23,053 --> 00:03:27,244 some more detail. We have here a porous barrier 54 00:03:27,244 --> 00:03:32,346 that the ions can flow freely from one side to the other. 55 00:03:32,346 --> 00:03:35,808 I reconnect them here, with a resistor, 56 00:03:35,808 --> 00:03:38,633 and so a current is now flowing. 57 00:03:38,633 --> 00:03:44,226 A current is flowing in this direction, through the 58 00:03:44,226 --> 00:03:48,872 resistor, from the plus side of the battery to the minus side, 59 00:03:48,872 --> 00:03:53,214 that means inside the battery, the current is flowing like 60 00:03:53,214 --> 00:03:57,479 this, and the electric field, here, is in this direction, 61 00:03:57,479 --> 00:04:01,059 from plus to minus, but also inside the battery, 62 00:04:01,059 --> 00:04:04,486 the electric field must be from plus to minus, 63 00:04:04,486 --> 00:04:06,924 so you see again, as we saw here, 64 00:04:06,924 --> 00:04:11,341 that the electric field is in the opposite direction of the 65 00:04:11,341 --> 00:04:14,236 current. You will have here S O 4 minus 66 00:04:14,236 --> 00:04:18,939 ions, and you have copper plus ions 67 00:04:18,939 --> 00:04:23,824 in this solution, and here you have zinc plus and 68 00:04:23,824 --> 00:04:28,913 you have S O 4 minus. And as current starts to run, 69 00:04:28,913 --> 00:04:32,373 S O 4 minus ions, which are now the 70 00:04:32,373 --> 00:04:38,378 current-carrier inside this battery, is going from the right 71 00:04:38,378 --> 00:04:42,754 -- they're going from the right to the left. 72 00:04:42,754 --> 00:04:49,291 Now why would S O 4 minus ions travel through an electric 73 00:04:49,291 --> 00:04:53,641 field that opposes them? That opposes their motion? 74 00:04:53,641 --> 00:04:56,86 And they do that because, in doing so, 75 00:04:56,86 --> 00:05:01,297 they engage in a chemical reaction which yields more 76 00:05:01,297 --> 00:05:05,387 energy than it costs to climb the electric hill. 77 00:05:05,387 --> 00:05:10,694 And while a current is flowing, while the S O 4 minus is going 78 00:05:10,694 --> 00:05:15,653 from the right to the left, you get fewer S O 4 minus ions 79 00:05:15,653 --> 00:05:19,267 here, this liquid here remains 80 00:05:19,267 --> 00:05:22,372 neutral, so copper plus must disappear. 81 00:05:22,372 --> 00:05:25,64 And it precipitates onto this copper bar. 82 00:05:25,64 --> 00:05:29,071 So it is like copper-plating. On this side, 83 00:05:29,071 --> 00:05:33,809 you get an increase of S O 4 minus, therefore you also must 84 00:05:33,809 --> 00:05:37,404 get an increase of zinc plus, because, again, 85 00:05:37,404 --> 00:05:41,734 this liquid there remains neutral, and that means that 86 00:05:41,734 --> 00:05:45,737 some of the zinc is being dissolved, so you get an 87 00:05:45,737 --> 00:05:50,177 increase in the concentration of the zinc. 88 00:05:50,177 --> 00:05:53,259 So the charge carriers inside this battery, 89 00:05:53,259 --> 00:05:56,855 the S O 4 minus ions, travel through this barrier, 90 00:05:56,855 --> 00:06:00,891 and they go from here to here, so they travel through an 91 00:06:00,891 --> 00:06:03,826 electric field that opposes their motion. 92 00:06:03,826 --> 00:06:07,495 And this happens at the expense of chemical energy. 93 00:06:07,495 --> 00:06:11,091 Now, when the copper solution becomes very dilute, 94 00:06:11,091 --> 00:06:15,053 because all the copper has been plated onto the copper, 95 00:06:15,053 --> 00:06:18,723 and when this becomes concentrated 96 00:06:18,723 --> 00:06:22,531 zinc plus, then the battery stops, and now what you can do, 97 00:06:22,531 --> 00:06:25,617 you can run a current in the opposite direction, 98 00:06:25,617 --> 00:06:28,769 so you can run a current, now, in this direction, 99 00:06:28,769 --> 00:06:32,512 you can force a current to run with another external power 100 00:06:32,512 --> 00:06:35,862 supply, and now the chemical reactions will reverse, 101 00:06:35,862 --> 00:06:38,817 so now, copper will go back into the solution, 102 00:06:38,817 --> 00:06:41,706 so it will dissolve, and now the zinc will be 103 00:06:41,706 --> 00:06:45,514 precipitated onto the zinc, and so now, if you do this long 104 00:06:45,514 --> 00:06:50,472 enough, you can run the battery again the way it is here. 105 00:06:50,472 --> 00:06:53,722 A car battery is exactly this kind of battery, 106 00:06:53,722 --> 00:06:57,982 except that you have lead and lead oxide instead of zinc and 107 00:06:57,982 --> 00:07:00,799 copper, but you also have sulfuric acid, 108 00:07:00,799 --> 00:07:04,41 like you have here, and a nickel-cadmium battery is 109 00:07:04,41 --> 00:07:08,743 well-known, you can charge that, too, those are the ones that 110 00:07:08,743 --> 00:07:12,498 are readily available in the stores, you can run your 111 00:07:12,498 --> 00:07:15,892 flashlights with these nickel-cadmium batteries. 112 00:07:15,892 --> 00:07:20,37 The symbol for battery that we will be using in our circuits is 113 00:07:20,37 --> 00:07:25,259 this, this is the positive side, 114 00:07:25,259 --> 00:07:31,591 and this is the negative side, this is a symbol that 115 00:07:31,591 --> 00:07:38,419 symbolizes that we are dealing with a -- with a battery. 116 00:07:38,419 --> 00:07:44,254 So let this point be B, and let this point be A, 117 00:07:44,254 --> 00:07:51,456 and here, we have a resistor R. So we have a current going, 118 00:07:51,456 --> 00:07:58,531 the current is going in this direction, a current I. 119 00:07:58,531 --> 00:08:03,45 This could be a light bulb, could be your laptop, 120 00:08:03,45 --> 00:08:08,471 could be a hair dryer, whatever, that you supply. 121 00:08:08,471 --> 00:08:13,903 If this R is not there, that means that the resistance 122 00:08:13,903 --> 00:08:18,719 is infinitely large, that means that the current 123 00:08:18,719 --> 00:08:23,946 that is running zero, then the voltage that we would 124 00:08:23,946 --> 00:08:31,23 measure over this battery, which is V B minus V A -- for 125 00:08:31,23 --> 00:08:36,297 which I will simply write down, V of the battery -- that 126 00:08:36,297 --> 00:08:40,72 voltage we call a curled E, which stands for EMF, 127 00:08:40,72 --> 00:08:45,88 which is electromotive force. I will show you that later. 128 00:08:45,88 --> 00:08:50,947 If I put a resistance R in here, which is not infinitely 129 00:08:50,947 --> 00:08:55,462 large, then a current will start to flow, but now, 130 00:08:55,462 --> 00:09:00,253 we should never forget, that between the points A and 131 00:09:00,253 --> 00:09:04,081 B, invisible to the human eye, 132 00:09:04,081 --> 00:09:09,225 there is always an internal resistance which I call little R 133 00:09:09,225 --> 00:09:13,497 of I, and so if a current starts to flow, it goes, 134 00:09:13,497 --> 00:09:18,205 not only through capital R, but it will also go through 135 00:09:18,205 --> 00:09:22,128 this little R, and so, according to Ohm's Law, 136 00:09:22,128 --> 00:09:26,836 the EMF is now I times the external resistance plus the 137 00:09:26,836 --> 00:09:30,236 internal one. The voltage that you would 138 00:09:30,236 --> 00:09:34,805 measure between point B and A is now 139 00:09:34,805 --> 00:09:37,642 going to change. That voltage, 140 00:09:37,642 --> 00:09:42,63 according to Ohm's Law, is I R, and so it's also the 141 00:09:42,63 --> 00:09:48,107 EMF minus I times R of I. And you see it's a little lower 142 00:09:48,107 --> 00:09:52,411 than the EMF. And the reason is this internal 143 00:09:52,411 --> 00:09:56,812 resistance here. If I shorted out this battery 144 00:09:56,812 --> 00:10:02,974 -- stupid thing to do -- but if I make R equal zero -- so I take 145 00:10:02,974 --> 00:10:08,389 the battery and I just short it out -- then, 146 00:10:08,389 --> 00:10:13,889 the maximum current that I can draw, then -- so R is now zero, 147 00:10:13,889 --> 00:10:19,48 so you can see that the maximum I that you can get is E divided 148 00:10:19,48 --> 00:10:23,988 by R of I -- and V of B, the voltage that you would 149 00:10:23,988 --> 00:10:28,226 measure now, between point B and A goes to zero. 150 00:10:28,226 --> 00:10:32,554 It doesn't mean that there is no current running, 151 00:10:32,554 --> 00:10:37,332 but it means that between these points, your potential 152 00:10:37,332 --> 00:10:41,156 difference goes down to zero. 153 00:10:41,156 --> 00:10:46,043 Shorting out a battery, of course, is not a very smart 154 00:10:46,043 --> 00:10:49,363 thing to do. You can put batteries in 155 00:10:49,363 --> 00:10:54,803 series, and thereby getting a higher potential difference -- 156 00:10:54,803 --> 00:10:59,506 this is the negative side, and this is the positive, 157 00:10:59,506 --> 00:11:03,563 I have an independent one, negative positive, 158 00:11:03,563 --> 00:11:07,436 and an independent one, negative, positive, 159 00:11:07,436 --> 00:11:13,394 each one, with an EMF E, and I can connect the positive 160 00:11:13,394 --> 00:11:17,239 side of one with the negative side of the other, 161 00:11:17,239 --> 00:11:21,492 just a conducting wire, and the positive side of this 162 00:11:21,492 --> 00:11:26,155 with the negative side of the other, and now the potential 163 00:11:26,155 --> 00:11:30,246 difference between these two points is now three E, 164 00:11:30,246 --> 00:11:33,6 open circuit, if I don't draw any current. 165 00:11:33,6 --> 00:11:36,545 If I draw a current, then, of course, 166 00:11:36,545 --> 00:11:40,062 I have to deal with the internal resistance. 167 00:11:40,062 --> 00:11:44,971 I'm going to build with you a copper-zinc battery of the kind 168 00:11:44,971 --> 00:11:49,212 that we just discussed. 169 00:11:49,212 --> 00:11:55,044 You see it here. Here's the copper -- copper 170 00:11:55,044 --> 00:11:59,52 sulfate solution, which H 2 S O 4, 171 00:11:59,52 --> 00:12:05,624 and here are my plates, this is my zinc plate, 172 00:12:05,624 --> 00:12:13,219 and this is my copper plate, and you are going to see the 173 00:12:13,219 --> 00:12:19,865 voltage displayed, I think, over there, 174 00:12:19,865 --> 00:12:25,045 that is correct -- there's no potential difference now, 175 00:12:25,045 --> 00:12:30,512 because they're not in place yet, and so here comes my my 176 00:12:30,512 --> 00:12:36,363 zinc, and here comes my copper, and they go into the solution, 177 00:12:36,363 --> 00:12:41,447 and you see about one volt. In general these potential 178 00:12:41,447 --> 00:12:45,283 difference are of that order of one volt. 179 00:12:45,283 --> 00:12:51,038 Oh point nine five. So now what I will do, 180 00:12:51,038 --> 00:12:57,396 I'm going to create a double one, so I have two independent 181 00:12:57,396 --> 00:13:03,753 batteries, I have here one whereby I have copper and zinc, 182 00:13:03,753 --> 00:13:09,562 and I have another one whereby I have copper and zinc, 183 00:13:09,562 --> 00:13:16,029 and I'm going to connect this one, and you will see now that 184 00:13:16,029 --> 00:13:24,688 the EMF will double. If we're ready for that -- 185 00:13:24,688 --> 00:13:27,862 this is my second one, it's going to be completely 186 00:13:27,862 --> 00:13:30,906 independent, so here comes the other two plates, 187 00:13:30,906 --> 00:13:34,598 make sure that I have the copper and the zinc not confused 188 00:13:34,598 --> 00:13:38,484 -- there we go -- and now you should see twice the potential. 189 00:13:38,484 --> 00:13:40,945 And you do see that. It's open circuit, 190 00:13:40,945 --> 00:13:44,443 there is no current running. Well, there is a s- minute 191 00:13:44,443 --> 00:13:48,264 little small current running through the volt meter that you 192 00:13:48,264 --> 00:13:50,531 see. But that's so small that that's 193 00:13:50,531 --> 00:13:54,093 -- can always be ignored. And you see you get double the 194 00:13:54,093 --> 00:13:57,487 EMF. Now what I will do -- so I 195 00:13:57,487 --> 00:14:01,222 have, now, about two volts between these two plates, 196 00:14:01,222 --> 00:14:05,176 two batteries in series, I now have a little light bulb 197 00:14:05,176 --> 00:14:08,472 here, and I'm going to turn on the light bulb. 198 00:14:08,472 --> 00:14:12,353 And now what you will see is that the voltage that you 199 00:14:12,353 --> 00:14:17,041 measure right here -- that's all you can do, you can only measure 200 00:14:17,041 --> 00:14:21,728 the voltage at the plates of the battery -- that now this voltage 201 00:14:21,728 --> 00:14:26,048 will drop, because of the internal resistance 202 00:14:26,048 --> 00:14:29,088 of the battery, in addition you will see some 203 00:14:29,088 --> 00:14:31,921 light, but that's really not my objective. 204 00:14:31,921 --> 00:14:34,546 For those of you who are sitting close, 205 00:14:34,546 --> 00:14:37,516 you can see this light bulb going to be lit. 206 00:14:37,516 --> 00:14:40,418 So I do this now, I can see the light bulb, 207 00:14:40,418 --> 00:14:43,803 a little bit of light, and notice that the voltage 208 00:14:43,803 --> 00:14:46,29 goes down. And so this value that you 209 00:14:46,29 --> 00:14:49,813 measure now, V of B, is now lower than the one point 210 00:14:49,813 --> 00:14:53,889 nine volts because of this term. You lose inside the battery 211 00:14:53,889 --> 00:15:00,873 through the internal resistance, you lose there potential 212 00:15:00,873 --> 00:15:03,9 difference. All right? 213 00:15:03,9 --> 00:15:11,542 So let's take this out, because this produces a lot of 214 00:15:11,542 --> 00:15:15,146 a lot of smelly fumes. OK. 215 00:15:15,146 --> 00:15:21,202 That's fine. If a charge moves from point A 216 00:15:21,202 --> 00:15:27,113 to point B, and here the potential is V A, 217 00:15:27,113 --> 00:15:36,933 and here the potential is V B, and a charge D Q moves -- and 218 00:15:36,933 --> 00:15:39,545 let's suppose, for simplicity, 219 00:15:39,545 --> 00:15:44,589 that V B minus V A -- yes, let's make the A larger than V 220 00:15:44,589 --> 00:15:49,633 B, that's just a little bit easier to think in that -- in 221 00:15:49,633 --> 00:15:52,425 those terms. It's not necessary, 222 00:15:52,425 --> 00:15:56,028 of course. So let's make V A large than V 223 00:15:56,028 --> 00:15:59 B. So the electric field is from A 224 00:15:59 --> 00:16:02,153 to B. And I move charge from A to B, 225 00:16:02,153 --> 00:16:07,017 then the electric field is doing work. 226 00:16:07,017 --> 00:16:11,057 And the work that the electric field is doing, 227 00:16:11,057 --> 00:16:15,457 D W, is the charge times the potential difference, 228 00:16:15,457 --> 00:16:19,857 which is V A minus V B. This work can be positive, 229 00:16:19,857 --> 00:16:24,436 if the charge is positive, it can be negative if the 230 00:16:24,436 --> 00:16:28,656 charge is negative, because we have assumed that 231 00:16:28,656 --> 00:16:31,35 this is positive, in this case. 232 00:16:31,35 --> 00:16:36,289 I can now do something that you shouldn't tell your math 233 00:16:36,289 --> 00:16:41,017 teachers, but physicists do it all the 234 00:16:41,017 --> 00:16:44,51 time, we divide by D T, and now we say, 235 00:16:44,51 --> 00:16:47,635 "Aha! What we have on the left side 236 00:16:47,635 --> 00:16:51,22 is now work per unit time. That's power. 237 00:16:51,22 --> 00:16:55,08 Joules per second." So this, now, is power. 238 00:16:55,08 --> 00:16:59,401 D Q D T is current, how many Coulombs per second 239 00:16:59,401 --> 00:17:01,607 flow. So this is current, 240 00:17:01,607 --> 00:17:04,456 I. And the potential difference, 241 00:17:04,456 --> 00:17:09,42 I simply call -- I use that symbol, V. 242 00:17:09,42 --> 00:17:14,195 So you see down here that the power delivered by a power 243 00:17:14,195 --> 00:17:19,144 supply is the current that it produces times the potential 244 00:17:19,144 --> 00:17:22,356 difference. And this is independent of 245 00:17:22,356 --> 00:17:27,479 Ohm's Law, this always holds. If you also include Ohm's Law, 246 00:17:27,479 --> 00:17:32,862 if you can use it -- last time, we discussed the limitations of 247 00:17:32,862 --> 00:17:37,376 Ohm's Law -- but if you can use it, and V equals I R, 248 00:17:37,376 --> 00:17:43,457 then of course, you can also write down for the 249 00:17:43,457 --> 00:17:49,813 power, that it is I squared R, and it is also V squared 250 00:17:49,813 --> 00:17:54,522 divided by R. Power is joules per second, 251 00:17:54,522 --> 00:17:59,348 but we write, for that, joules per second, 252 00:17:59,348 --> 00:18:04,292 we write for that, watts, just a capital W, 253 00:18:04,292 --> 00:18:10,178 but it's named after the physicist Watt. 254 00:18:10,178 --> 00:18:14,785 So we always express the power in terms of watts. 255 00:18:14,785 --> 00:18:20,735 So suppose we have a resistance R, and we run a current through 256 00:18:20,735 --> 00:18:26,494 it -- this is the resistance -- e run a current I through it, 257 00:18:26,494 --> 00:18:31,485 and let us take an example, that the current I is one 258 00:18:31,485 --> 00:18:36,284 ampere, and that the resistance is one hundred ohm. 259 00:18:36,284 --> 00:18:41,467 Then the power which is dissipated in this resistor has 260 00:18:41,467 --> 00:18:45,558 to be provided by your battery, 261 00:18:45,558 --> 00:18:49,027 that power P is now one hundred watts. 262 00:18:49,027 --> 00:18:52,308 I square R, if you want to use this. 263 00:18:52,308 --> 00:18:56,527 If it is two amperes, and you don't change the 264 00:18:56,527 --> 00:19:00,839 resistance, then it becomes four hundred watts. 265 00:19:00,839 --> 00:19:05,057 Because it's I square R. I doubles, the power, 266 00:19:05,057 --> 00:19:09,932 and four times higher. Now, this energy is dissipated 267 00:19:09,932 --> 00:19:15,651 in the form of heat, and if it gets hot enough, 268 00:19:15,651 --> 00:19:20,493 then maybe you can produce light, that's the idea behind a 269 00:19:20,493 --> 00:19:23,551 light bulb. The filament into -- in a 270 00:19:23,551 --> 00:19:27,799 tungsten incandescent light bulb becomes very high, 271 00:19:27,799 --> 00:19:32,472 twenty five hundred degrees Centigrade, maybe even three 272 00:19:32,472 --> 00:19:36,89 thousand -- not so high, of course, that the tungsten 273 00:19:36,89 --> 00:19:40,203 melts -- and so, you begin to see light. 274 00:19:40,203 --> 00:19:44,026 So, for instance, a hundred watt light bulb -- 275 00:19:44,026 --> 00:19:49,293 oh, unintelligible work on here -- so if we have a hundred watt 276 00:19:49,293 --> 00:19:53,765 light bulb in your dormitory, 277 00:19:53,765 --> 00:20:00,782 and the voltage is hundred ten volts, you just plug it into the 278 00:20:00,782 --> 00:20:07,346 wall, then the current that will run is about oh point nine 279 00:20:07,346 --> 00:20:09,722 amperes. P equals V I. 280 00:20:09,722 --> 00:20:16,399 This product must be a hundred. And then the resistance that 281 00:20:16,399 --> 00:20:22,51 you have is about a hundred and twenty ohms. 282 00:20:22,51 --> 00:20:26,116 V equals I R. So even though it's quite hot 283 00:20:26,116 --> 00:20:31,094 -- a light bulb -- the amount of light that it produces is, 284 00:20:31,094 --> 00:20:35,73 in general, not more than twenty percent of this power. 285 00:20:35,73 --> 00:20:40,279 It's not a very efficient thing, an incandescent light 286 00:20:40,279 --> 00:20:42,94 bulb. A fluorescent tube is much 287 00:20:42,94 --> 00:20:45,859 better. So if you have a forty watt 288 00:20:45,859 --> 00:20:49,721 fluorescent tube, you can much more light that 289 00:20:49,721 --> 00:20:54,958 you get out of a forty watt incandescent bulb. 290 00:20:54,958 --> 00:20:59,477 If we take your heaters that you have in your dormitories - 291 00:20:59,477 --> 00:21:03,529 typically two kilowatts, but let's make it twenty two 292 00:21:03,529 --> 00:21:06,724 hundred watts, because that divides nicely 293 00:21:06,724 --> 00:21:11,633 through a hundred and ten volts -- so then you would have twenty 294 00:21:11,633 --> 00:21:14,282 amperes -- that's a lot of amperes. 295 00:21:14,282 --> 00:21:18,646 If the dormitory is very old, chances are that your fuses 296 00:21:18,646 --> 00:21:21,373 will go. Twenty amperes is more than 297 00:21:21,373 --> 00:21:25,425 many houses can handle. But nowadays, 298 00:21:25,425 --> 00:21:29,627 I think most outlets are good for twenty five amperes or so. 299 00:21:29,627 --> 00:21:33,4 But not for much more. And so, now you have a resistor 300 00:21:33,4 --> 00:21:36,961 in your heater which is about five point five ohms. 301 00:21:36,961 --> 00:21:40,022 Just to give you a feeling for some numbers. 302 00:21:40,022 --> 00:21:44,366 N ow, you want heat out of your heater, and you want light out 303 00:21:44,366 --> 00:21:47,356 of your light bulb, so you want to keep the 304 00:21:47,356 --> 00:21:51,486 temperature of your heater modest, not so high that you get 305 00:21:51,486 --> 00:21:54,69 a lot of light. If you make it two thousand or 306 00:21:54,69 --> 00:21:59,329 twenty five hundred degrees, then you would get a lot of 307 00:21:59,329 --> 00:22:02,091 light out of your heater. And so suppose that half of 308 00:22:02,091 --> 00:22:04,376 that power would come out in terms of light, 309 00:22:04,376 --> 00:22:07,51 and you turn on your heater it night, would be like having a 310 00:22:07,51 --> 00:22:10,857 thousand-watt light bulb in your dormitory, you don't want that. 311 00:22:10,857 --> 00:22:12,876 So how do you do -- what do you do now? 312 00:22:12,876 --> 00:22:15,161 Well, you simply keep the temperature about, 313 00:22:15,161 --> 00:22:17,87 maybe, thousand degrees Centigrade, it gets a little 314 00:22:17,87 --> 00:22:20,951 red-hot, very little light is produced, and how do you keep 315 00:22:20,951 --> 00:22:23,501 the temperature low? Well, you could cool it with 316 00:22:23,501 --> 00:22:27,327 air, some of these heaters have fans that cool them. 317 00:22:27,327 --> 00:22:30,334 Or you just make the resistance, you do both, 318 00:22:30,334 --> 00:22:33,546 very large, huge surface area of the resistance, 319 00:22:33,546 --> 00:22:36,894 not small, but large, and so now they have a large 320 00:22:36,894 --> 00:22:40,585 surface area so they can radiate their heat, and so the 321 00:22:40,585 --> 00:22:43,934 temperature remains low. So if you look at your -- 322 00:22:43,934 --> 00:22:47,351 things that you have at home, you have light bulbs, 323 00:22:47,351 --> 00:22:50,084 forty to two hundred watts, your toaster, 324 00:22:50,084 --> 00:22:53,775 maybe three hundred watts. Your cooking plates and your 325 00:22:53,775 --> 00:22:57,534 heaters, something like two kilowatts, 326 00:22:57,534 --> 00:23:00,482 TV, a few hundred watts, your electric toothbrush 327 00:23:00,482 --> 00:23:02,754 probably only four watts, very modest. 328 00:23:02,754 --> 00:23:06,378 Your own body produces about hundred watts heat -- of course 329 00:23:06,378 --> 00:23:09,203 that's -- energy. You have a very large surface 330 00:23:09,203 --> 00:23:12,827 area, so you don't get nearly as hot as a hundred-watt light 331 00:23:12,827 --> 00:23:16,451 bulb, because your surface area is large, so you only have a 332 00:23:16,451 --> 00:23:19,644 modest ninety-eight degrees Fahrenheit, unless you're 333 00:23:19,644 --> 00:23:22,531 running a fever. So you don't produce any light, 334 00:23:22,531 --> 00:23:25,786 because you're not hot enough for that, so you produce 335 00:23:25,786 --> 00:23:29,733 infrared radiation, and that's very 336 00:23:29,733 --> 00:23:33,343 noticeable. You hold someone in your arms, 337 00:23:33,343 --> 00:23:37,128 the good feeling is, you feel the body heat. 338 00:23:37,128 --> 00:23:41,882 That's the infrared radiation. That radiates at about a 339 00:23:41,882 --> 00:23:45,404 hundred joules per second. Hundred watts. 340 00:23:45,404 --> 00:23:48,837 An electric blanket is only fifty watts. 341 00:23:48,837 --> 00:23:53,591 So a partner is about twice as effective as an electric 342 00:23:53,591 --> 00:23:57,376 blanket. Maybe also more fun. 343 00:23:57,376 --> 00:24:03,372 The power delivered by a battery is the current that the 344 00:24:03,372 --> 00:24:08,058 battery delivers times E, which is this EMF. 345 00:24:08,058 --> 00:24:13,944 And so when a current is running, it is I squared times 346 00:24:13,944 --> 00:24:20,048 the sum of the two resistances. The external one plus the 347 00:24:20,048 --> 00:24:24,191 internal one. We can never bypass that. 348 00:24:24,191 --> 00:24:28,877 The heat that is produced in the 349 00:24:28,877 --> 00:24:34,07 external one is I squared capital R, but the heat that is 350 00:24:34,07 --> 00:24:38,614 produced inside the battery is I squared little R, 351 00:24:38,614 --> 00:24:42,972 you can't avoid that. And so if you make R zero, 352 00:24:42,972 --> 00:24:48,442 by shorting out the battery, then you get a current which is 353 00:24:48,442 --> 00:24:54,377 the maximum current that you can get, which is the EMF divided by 354 00:24:54,377 --> 00:24:59,199 R of I -- so you've killed the capital R, 355 00:24:59,199 --> 00:25:05,375 it's zero now -- and so -- so you get a power which is the 356 00:25:05,375 --> 00:25:10,143 maximum power, which is now E squared divided 357 00:25:10,143 --> 00:25:14,585 by R of I. I maximum squared times R of I. 358 00:25:14,585 --> 00:25:19,461 It's the same thing, it is the maximum current 359 00:25:19,461 --> 00:25:24,337 square times R of I, and all of that comes out 360 00:25:24,337 --> 00:25:29,538 inside the battery. Nothing comes out outside it. 361 00:25:29,538 --> 00:25:34,414 If you have a nine-volt Duracell 362 00:25:34,414 --> 00:25:39,029 battery, the ones that we're all so familiar with, 363 00:25:39,029 --> 00:25:43,833 so then E is about nine volts, the EMF, the internal 364 00:25:43,833 --> 00:25:48,165 resistance of such a battery is about two ohms, 365 00:25:48,165 --> 00:25:53,439 and so the maximum current that you can ever get out of a 366 00:25:53,439 --> 00:25:58,619 Duracell battery would be about four and a half amperes, 367 00:25:58,619 --> 00:26:02,763 that is I Max, would be about four and a half 368 00:26:02,763 --> 00:26:07,377 amperes, and so P Max would be about 369 00:26:07,377 --> 00:26:10,56 forty watts. So if you take a nine-volt 370 00:26:10,56 --> 00:26:15,334 battery, and you short it out, then the battery should get 371 00:26:15,334 --> 00:26:19,605 warm, because all that heat, all that forty watts is 372 00:26:19,605 --> 00:26:24,547 generated inside your battery. The value for V of B that you 373 00:26:24,547 --> 00:26:29,488 measured would go down to zero, if you really could short it 374 00:26:29,488 --> 00:26:33,341 out, with a resistor which has zero resistance. 375 00:26:33,341 --> 00:26:38,534 Now it's, of course, a pretty stupid thing to do, 376 00:26:38,534 --> 00:26:42,088 to short out a battery, but it's not dangerous. 377 00:26:42,088 --> 00:26:45,256 Forty watts, the thing gets a little warm, 378 00:26:45,256 --> 00:26:47,11 big deal. So let's do it. 379 00:26:47,11 --> 00:26:49,274 So I have, here, the voltage, 380 00:26:49,274 --> 00:26:52,674 that you can see, that we measure a nine-volt 381 00:26:52,674 --> 00:26:55,842 Duracell battery, I have the battery here. 382 00:26:55,842 --> 00:27:00,092 And you can read it here. I hope the decimal point is in 383 00:27:00,092 --> 00:27:03,337 there, but it's about nine point six volts. 384 00:27:03,337 --> 00:27:06,505 And now I am going to do something stupid, 385 00:27:06,505 --> 00:27:09,98 but, again, it's not dangerous -- 386 00:27:09,98 --> 00:27:13,557 I'm going to take my car keys and I'm going to short out the 387 00:27:13,557 --> 00:27:15,861 battery. So simply connect point A with 388 00:27:15,861 --> 00:27:19,681 point B, and so the voltage that you're going to see is going -- 389 00:27:19,681 --> 00:27:22,833 maybe not go to zero, exactly, because my key may not 390 00:27:22,833 --> 00:27:25,744 have zero resistance, but it goes very low -- and 391 00:27:25,744 --> 00:27:28,775 what you cannot experience is something that I can, 392 00:27:28,775 --> 00:27:32,17 that this battery will get hot. These forty watts will be 393 00:27:32,17 --> 00:27:34,413 generated inside here. It is possible, 394 00:27:34,413 --> 00:27:37,809 though, that when the battery gets hot, that the internal 395 00:27:37,809 --> 00:27:41,104 resistance may even go up a little 396 00:27:41,104 --> 00:27:43,992 because, remember that resistance goes up when 397 00:27:43,992 --> 00:27:46,174 temperature goes up, in which case, 398 00:27:46,174 --> 00:27:49,639 the power will go down, so it may not be the full forty 399 00:27:49,639 --> 00:27:52,014 watts. But I can assure you that I can 400 00:27:52,014 --> 00:27:55,351 feel this thing getting warm. So let me short it out, 401 00:27:55,351 --> 00:27:56,827 now. I'm doing this now. 402 00:27:56,827 --> 00:27:59,266 And you read the voltage, I can see it, 403 00:27:59,266 --> 00:28:02,154 too here -- oh, it's always not so easy with a 404 00:28:02,154 --> 00:28:04,529 key to do that -- here, it's very low, 405 00:28:04,529 --> 00:28:07,545 hey, look at that. It's about a tenth of a volt, 406 00:28:07,545 --> 00:28:09,663 and I feel this thing getting hot. 407 00:28:09,663 --> 00:28:13 It's really warming up, now. 408 00:28:13 --> 00:28:15,044 And so I'm ruining this battery. 409 00:28:15,044 --> 00:28:18,802 This is a terrible thing to do, batteries don't like that. 410 00:28:18,802 --> 00:28:22,099 But, when I take off the unintelligible resistance, 411 00:28:22,099 --> 00:28:25,527 some of that may come back. It may not be permanently 412 00:28:25,527 --> 00:28:28,823 damaged, and you see, it's already eight and a half 413 00:28:28,823 --> 00:28:31,197 volts. So there's no way that you can 414 00:28:31,197 --> 00:28:34,164 start a car with a nine-volt Duracell battery, 415 00:28:34,164 --> 00:28:38,119 because you just can't get the current that you need for your 416 00:28:38,119 --> 00:28:41,086 starter engine. Your starter motor needs a few 417 00:28:41,086 --> 00:28:45,752 hundred amperes. If you take a car battery, 418 00:28:45,752 --> 00:28:50,47 that's about twelve volts. It has a very low internal 419 00:28:50,47 --> 00:28:54,371 resistance, of about one-fiftieth of an ohm. 420 00:28:54,371 --> 00:28:59,452 So that means that the maximum current that you can draw, 421 00:28:59,452 --> 00:29:04,079 if you short-circuit it, would be something like six 422 00:29:04,079 --> 00:29:07,799 hundred amperes. And so the maximum power, 423 00:29:07,799 --> 00:29:11,519 if you were so stupid to short-circuit it, 424 00:29:11,519 --> 00:29:15,874 that would all be generated inside 425 00:29:15,874 --> 00:29:19,292 the battery, would be something like seven 426 00:29:19,292 --> 00:29:22,543 kilowatts. If you ever work on your car, 427 00:29:22,543 --> 00:29:27,296 make sure that you never drop accidentally the wrench that 428 00:29:27,296 --> 00:29:31,381 you're using onto the battery. Because if you did, 429 00:29:31,381 --> 00:29:35,049 then inside the battery, about six kilowatts, 430 00:29:35,049 --> 00:29:39,801 seven thousand joules per second, are going to be produced 431 00:29:39,801 --> 00:29:43,72 in terms of heat, and the sulfuric acid is going 432 00:29:43,72 --> 00:29:49,539 to boil, the case may melt, and that's no good. 433 00:29:49,539 --> 00:29:56,003 Not only is that stupid, but it's also very dangerous. 434 00:29:56,003 --> 00:29:59,417 So let's do it. I have, here, 435 00:29:59,417 --> 00:30:02,954 this battery, and I have here, 436 00:30:02,954 --> 00:30:05,881 the wrench. Just in case. 437 00:30:05,881 --> 00:30:12,345 I'm going to short out that battery, and as I do that, 438 00:30:12,345 --> 00:30:20,394 you will clearly see that the battery doesn't like it. 439 00:30:20,394 --> 00:30:25,38 I will be very careful not to hold on to this wrench too long, 440 00:30:25,38 --> 00:30:30,284 because it would weld onto it, actually, it can weld on to it 441 00:30:30,284 --> 00:30:33,39 and stay there, the current is so high, 442 00:30:33,39 --> 00:30:38,049 it can go up to six hundred amperes, that it can weld onto 443 00:30:38,049 --> 00:30:41,482 it, and then you can't get it off any more. 444 00:30:41,482 --> 00:30:45,16 In case that happens, I will walk out of here. 445 00:30:45,16 --> 00:30:47,694 And I advise you to do the same. 446 00:30:47,694 --> 00:30:48,756 You ready? OK. 447 00:30:48,756 --> 00:30:51,536 I go now. You see? 448 00:30:51,536 --> 00:30:54,807 That's what happens. A very high current, 449 00:30:54,807 --> 00:30:58,323 and when you do this too often to batteries, 450 00:30:58,323 --> 00:31:02,821 they're not going to live very long, they don't like it. 451 00:31:02,821 --> 00:31:07,483 But I wasn't joking when I said, when you work on the car, 452 00:31:07,483 --> 00:31:12,144 that you should avoid this, because I have seen it happen, 453 00:31:12,144 --> 00:31:16,151 that wrenches actually welded onto the terminals. 454 00:31:16,151 --> 00:31:20,567 Your electric company charges you 455 00:31:20,567 --> 00:31:24,023 for energy, they don't care about the power, 456 00:31:24,023 --> 00:31:28,764 how many joules you use second, but they care about how much 457 00:31:28,764 --> 00:31:32,3 energy you're using. So they will charge you, 458 00:31:32,3 --> 00:31:34,469 then, for joules, you think. 459 00:31:34,469 --> 00:31:37,844 That's energy. However, if you look at your 460 00:31:37,844 --> 00:31:41,461 bill, you're being charged for kilowatt-hours. 461 00:31:41,461 --> 00:31:45,559 Well, a kilo is thousands, and an hour is thirty six 462 00:31:45,559 --> 00:31:50,22 hundred seconds, so the units of energy for 463 00:31:50,22 --> 00:31:53,381 which they charge you is this in joules. 464 00:31:53,381 --> 00:31:56,137 Two thousand watts. Cooking plates, 465 00:31:56,137 --> 00:32:00,19 you run for two hours, that is four kilowatt-hours. 466 00:32:00,19 --> 00:32:04,973 They will probably charge you ten cents per kilowatt-hour -- 467 00:32:04,973 --> 00:32:09,918 for that same amount of money, you could run your hundred-watt 468 00:32:09,918 --> 00:32:14,457 light bulb for forty hours. Again, that would be the same 469 00:32:14,457 --> 00:32:19,078 four kilowatt hours -- or, you could brush your teeth with 470 00:32:19,078 --> 00:32:24,672 your electric toothbrush for about one thousand hours. 471 00:32:24,672 --> 00:32:33,271 Now I want to take a look with you at a network which consists 472 00:32:33,271 --> 00:32:41,165 of resistors and batteries. And this is the kind of stuff 473 00:32:41,165 --> 00:32:46,945 that you see on homework assignments, and, 474 00:32:46,945 --> 00:32:53,853 perhaps, on exams. And so now, we start out with a 475 00:32:53,853 --> 00:32:59,121 very modest circuit, here we have a 476 00:32:59,121 --> 00:33:03,699 resistance R 1, here we have a resistor R 2, 477 00:33:03,699 --> 00:33:08,064 and here R 3, and then we put a battery in 478 00:33:08,064 --> 00:33:13,175 here, and we put the plus side, say, on the left, 479 00:33:13,175 --> 00:33:16,582 this the plus side, a minus side, 480 00:33:16,582 --> 00:33:22,012 and let the potential difference of this one be V 2. 481 00:33:22,012 --> 00:33:28,613 It's really the EMF, but I will ignore any kind of 482 00:33:28,613 --> 00:33:33,132 internal resistance of the batteries, it's completely 483 00:33:33,132 --> 00:33:38,085 negligible in this problem. And here I put also a battery, 484 00:33:38,085 --> 00:33:43,3 let this be the negative side, and this be the positive side, 485 00:33:43,3 --> 00:33:46,689 and let the potential difference be V 1. 486 00:33:46,689 --> 00:33:50,861 And so, imagine that you know V 1, V 2, R 1, R 2, 487 00:33:50,861 --> 00:33:54,076 and R 3. But what I'm going to ask you 488 00:33:54,076 --> 00:33:56,51 is, what is I 1, what is I 2, 489 00:33:56,51 --> 00:33:59,725 and what is I 3? I want the magnitude, 490 00:33:59,725 --> 00:34:03,21 and I want the direction. 491 00:34:03,21 --> 00:34:07,451 When you look at this, it's by no means obvious that 492 00:34:07,451 --> 00:34:12,275 the current in this resistor will be to the right or to the 493 00:34:12,275 --> 00:34:17,098 left, it's by no means obvious, it depends on the -- on the 494 00:34:17,098 --> 00:34:20,508 values V 1 and V2, and on the resistances. 495 00:34:20,508 --> 00:34:25,415 The basic idea behind solving these problems are in what we 496 00:34:25,415 --> 00:34:29,656 call Kirchoff's rules. Kirchoff's first rule is that 497 00:34:29,656 --> 00:34:34,48 the closed loop integral over a closed loop of E dot D L is 498 00:34:34,48 --> 00:34:38,339 zero. We've seen that before. 499 00:34:38,339 --> 00:34:41,665 I don't know why Kirchoff gets the credit for this. 500 00:34:41,665 --> 00:34:45,591 This always is the case when we're dealing with conservative 501 00:34:45,591 --> 00:34:48,053 fields. When you start at a particular 502 00:34:48,053 --> 00:34:51,645 point, you go around E dot D L, you're back at the same 503 00:34:51,645 --> 00:34:55,172 potential where you were before, so this must be zero, 504 00:34:55,172 --> 00:34:58,099 as long as you deal with conservative fields. 505 00:34:58,099 --> 00:35:01,825 So that's his first rule. And you can do this closed loop 506 00:35:01,825 --> 00:35:04,021 anywhere. You can even do it here. 507 00:35:04,021 --> 00:35:08,415 It would still be zero. You can do it here. 508 00:35:08,415 --> 00:35:11,047 Also zero. You can do it there. 509 00:35:11,047 --> 00:35:15,959 No matter where you do it, that closed loop integral must 510 00:35:15,959 --> 00:35:19,117 be zero. And then there is the second 511 00:35:19,117 --> 00:35:23,24 Kirchoff's rule, and that is what we call charge 512 00:35:23,24 --> 00:35:26,661 conservation. If there is a steady-state 513 00:35:26,661 --> 00:35:30,608 situation, then, independent of which junction 514 00:35:30,608 --> 00:35:36,309 you go to, the current that flows in must flow out. 515 00:35:36,309 --> 00:35:40,635 Can't have a pile-up of charge. That's the second rule. 516 00:35:40,635 --> 00:35:43,598 And I gave you a problem, three seven, 517 00:35:43,598 --> 00:35:46,802 to work out, and you can look in the book 518 00:35:46,802 --> 00:35:50,487 how that is done. However, I'm going to work on 519 00:35:50,487 --> 00:35:55,052 this with you in a slightly different way than the book is 520 00:35:55,052 --> 00:35:58,416 doing it, which I, personally, like better. 521 00:35:58,416 --> 00:36:02,261 But it may confuse you. So I warn you in advance, 522 00:36:02,261 --> 00:36:06,746 you may not want to use my method at all. 523 00:36:06,746 --> 00:36:11,489 What I do is the following. I say, OK, I assume that there 524 00:36:11,489 --> 00:36:14,318 is a closed loop current here, I 1. 525 00:36:14,318 --> 00:36:17,979 And that there is a closed loop current here, 526 00:36:17,979 --> 00:36:20,807 I 2. Whether I make them clockwise, 527 00:36:20,807 --> 00:36:23,719 or counterclockwise, is unimportant. 528 00:36:23,719 --> 00:36:27,297 I could have chosen one clockwise, the other 529 00:36:27,297 --> 00:36:29,71 counterclockwise, unimportant. 530 00:36:29,71 --> 00:36:34,286 However, once I choose a direction, it has consequences, 531 00:36:34,286 --> 00:36:39,507 as you will see. And that's all that's running. 532 00:36:39,507 --> 00:36:43,716 One current like this, and one current independently 533 00:36:43,716 --> 00:36:45,944 like that. If I assume that, 534 00:36:45,944 --> 00:36:49,41 then I have automatically -- automatically, 535 00:36:49,41 --> 00:36:54,113 I am obeying the second rules, because a current that goes 536 00:36:54,113 --> 00:36:56,754 around is -- charge conservation, 537 00:36:56,754 --> 00:36:59,56 right? There's no charge piling up. 538 00:36:59,56 --> 00:37:03,521 So the second rule of Kirchoff is already obeyed. 539 00:37:03,521 --> 00:37:07,234 So now I go to the first one, and I can start, 540 00:37:07,234 --> 00:37:11,496 now, at any point in that circuit, 541 00:37:11,496 --> 00:37:15,1 and go around -- I can go around clockwise, 542 00:37:15,1 --> 00:37:17,846 I can go around counterclockwise, 543 00:37:17,846 --> 00:37:22,996 it makes no difference as long as I return to the same point, 544 00:37:22,996 --> 00:37:26,085 that integral E dot D L must be zero. 545 00:37:26,085 --> 00:37:29,089 I'm returning at the same potential. 546 00:37:29,089 --> 00:37:34,152 What is the integral of E dot D L in going from point one to 547 00:37:34,152 --> 00:37:37,242 point two? Well, that's the potential 548 00:37:37,242 --> 00:37:42,177 difference between point one and point two. 549 00:37:42,177 --> 00:37:46,017 And so let us start here, and let us go around, 550 00:37:46,017 --> 00:37:50,19 and we have to adopt a certain convention, namely, 551 00:37:50,19 --> 00:37:54,615 if we go up in potential, and we go down in potential. 552 00:37:54,615 --> 00:37:58,621 Again, you're free to choose the sign convention. 553 00:37:58,621 --> 00:38:02,127 But I would say, when I go up in potential, 554 00:38:02,127 --> 00:38:06,468 I give that a plus sign, when I go down in potential, 555 00:38:06,468 --> 00:38:11,726 I give that a minus sign. So I start here. 556 00:38:11,726 --> 00:38:15,677 I could have started there, I could have started there, 557 00:38:15,677 --> 00:38:19,335 makes no difference, as long as I don't start here, 558 00:38:19,335 --> 00:38:21,969 that makes no sense. So I start here, 559 00:38:21,969 --> 00:38:24,896 and I go around like this. So right here, 560 00:38:24,896 --> 00:38:26,871 I go down in potential, V 1. 561 00:38:26,871 --> 00:38:30,309 So I get minus V 1. Now I go with current I 1 in 562 00:38:30,309 --> 00:38:32,724 the direction, from left to right, 563 00:38:32,724 --> 00:38:36,455 so that means that the potential here must be higher 564 00:38:36,455 --> 00:38:38,211 than there. V equals I R. 565 00:38:38,211 --> 00:38:42,601 Potential here must be higher than there. 566 00:38:42,601 --> 00:38:47,365 So I go down in potential, so I get minus I 1, 567 00:38:47,365 --> 00:38:50,012 R 1. Now I go through R 3. 568 00:38:50,012 --> 00:38:53,4 This current, I 1, is going down, 569 00:38:53,4 --> 00:38:59,329 so this has a higher potential that here, so I go down in 570 00:38:59,329 --> 00:39:03,458 potential, so I get minus I 1 times R 3. 571 00:39:03,458 --> 00:39:08,963 But I have, independently, a current I 2 which is now 572 00:39:08,963 --> 00:39:13,833 coming towards me when I go down. 573 00:39:13,833 --> 00:39:18,33 And so if it comes towards me, that current would give me an 574 00:39:18,33 --> 00:39:21,911 increase in potential. This would have to have a 575 00:39:21,911 --> 00:39:26,103 higher potential than this, for this current to do this. 576 00:39:26,103 --> 00:39:30,523 So now I climb up the potential hill, so I get now plus I 2 577 00:39:30,523 --> 00:39:34,333 times R 3 recording slows down. normal speed Uh-oh, 578 00:39:34,333 --> 00:39:37,305 look what I did, I wrote down capital R, 579 00:39:37,305 --> 00:39:40,963 clearly I meant R 1, there is no capital R in the 580 00:39:40,963 --> 00:39:44,393 whole problem. Sorry for that, 581 00:39:44,393 --> 00:39:47,366 you should read this as minus I 1, R 1. 582 00:39:47,366 --> 00:39:51,278 recording starts slow, speeds up to normal I'm back 583 00:39:51,278 --> 00:39:55,268 where I was, because these wires have no resistance. 584 00:39:55,268 --> 00:39:58,632 And so I'm back where I am, so this is zero. 585 00:39:58,632 --> 00:40:01,996 One equation with two unknowns, I 1 and I 2. 586 00:40:01,996 --> 00:40:04,5 So now, let's go around this one. 587 00:40:04,5 --> 00:40:08,177 We can go clockwise, we can go counterclockwise, 588 00:40:08,177 --> 00:40:11,072 makes no difference. Let's start here, 589 00:40:11,072 --> 00:40:15,648 and I go in this direction, once around. 590 00:40:15,648 --> 00:40:20,935 So now, I go through R 3, and this current I 2 is running 591 00:40:20,935 --> 00:40:25,09 in this direction, so I go down in potential. 592 00:40:25,09 --> 00:40:30,189 So I get minus I 2 times R 3. But current I 1 is coming 593 00:40:30,189 --> 00:40:33,777 towards me. [inaudible] if I go in this 594 00:40:33,777 --> 00:40:39,726 direction, I 1 is coming towards me, so I climb up the potential 595 00:40:39,726 --> 00:40:42,842 hill. So I got plus I 1 times R 3. 596 00:40:42,842 --> 00:40:49,556 Now I go through R 3 in this direction, current I 2 is also 597 00:40:49,556 --> 00:40:53,954 in this direction, and so this must have a higher 598 00:40:53,954 --> 00:40:58,536 potential that this, so I go downhill in potential, 599 00:40:58,536 --> 00:41:03,392 so I have minus I 2 times R 2. I come down here -- ah, 600 00:41:03,392 --> 00:41:07,515 here's a battery. And it goes up in potential. 601 00:41:07,515 --> 00:41:10,63 So I get plus V 2, and that's zero. 602 00:41:10,63 --> 00:41:13,471 Two equations with two unknowns. 603 00:41:13,471 --> 00:41:17,502 I can solve for I 1, and I can solve for I 2. 604 00:41:17,502 --> 00:41:23,06 So I 1 and I 2 pop out. Let us assume that I 1 is 605 00:41:23,06 --> 00:41:25,681 positive, I find a positive value. 606 00:41:25,681 --> 00:41:28,777 It means, it's really in this direction. 607 00:41:28,777 --> 00:41:31,477 Let's suppose that I 1 is negative. 608 00:41:31,477 --> 00:41:35,923 I find minus three amperes. Well, it means that I 1 is in 609 00:41:35,923 --> 00:41:37,828 this direction, big deal. 610 00:41:37,828 --> 00:41:41,322 And so the whole operation is sign sensitive. 611 00:41:41,322 --> 00:41:45,054 And the same is true here. If I two is positive, 612 00:41:45,054 --> 00:41:47,515 it means it's in this direction. 613 00:41:47,515 --> 00:41:51,247 If I 2 is negative, then it's in that direction. 614 00:41:51,247 --> 00:41:55,137 How about I 3 now? Well, let us assume that I 1 is 615 00:41:55,137 --> 00:42:01,321 plus three amperes, and that you find that I 2 is 616 00:42:01,321 --> 00:42:04,552 plus one ampere. That's possible, 617 00:42:04,552 --> 00:42:07,48 right? You have two equations, 618 00:42:07,48 --> 00:42:11,418 two unknowns, and these are the answers. 619 00:42:11,418 --> 00:42:16,264 So three amperes goes like this [wssshhht], down, 620 00:42:16,264 --> 00:42:20,404 and one ampere comes up. Well, it's clear, 621 00:42:20,404 --> 00:42:25,049 then, that I 3 is three minus one, is plus two. 622 00:42:25,049 --> 00:42:30,703 Another way of looking at it is, three amperes come in at 623 00:42:30,703 --> 00:42:34,963 this juncture, I 2 is one ampere, 624 00:42:34,963 --> 00:42:38,725 so one ampere goes through, so two must go down. 625 00:42:38,725 --> 00:42:41,606 That's really Kirchoff's second rule. 626 00:42:41,606 --> 00:42:45,847 If I 1 were plus one ampere, and I 2 was also plus one 627 00:42:45,847 --> 00:42:50,729 ampere, then I 3 will be zero. No current would flow through I 628 00:42:50,729 --> 03. 629 03. --> 00:42:53,37 But my method would still work. 630 00:42:53,37 --> 00:42:57,611 I find one ampere going down, and one ampere going up, 631 00:42:57,611 --> 00:43:02,333 so there's no -- no current going through R th- there's only 632 00:43:02,333 --> 00:43:06,093 current going in this direction, 633 00:43:06,093 --> 00:43:09,052 one ampere. And we're recording slows. 634 00:43:09,052 --> 00:43:11,851 normal speed Uh-oh, look what I did, 635 00:43:11,851 --> 00:43:16,249 I wrote down I 1 R -- there is no capital R in the whole 636 00:43:16,249 --> 00:43:18,888 problem, I clearly meant I 1, R 1. 637 00:43:18,888 --> 00:43:22,167 So read minus I one R one. Sorry for that. 638 00:43:22,167 --> 00:43:25,366 starts slow, speeds up to normal I'm back 639 00:43:25,366 --> 00:43:29,444 where I was, because these wires have no resistance. 640 00:43:29,444 --> 00:43:32,883 And so I'm back where I am, so this is zero. 641 00:43:32,883 --> 00:43:37,957 One equation with two unknowns, I 1 and I 2. 642 00:43:37,957 --> 00:43:41,038 So now, let's go around this one. 643 00:43:41,038 --> 00:43:45,564 We can go clockwise, we can go counterclockwise, 644 00:43:45,564 --> 00:43:49,127 makes no difference. Let's start here, 645 00:43:49,127 --> 00:43:52,883 and I go in this direction, once around. 646 00:43:52,883 --> 00:43:58,275 So now, I go through R 3, and this current I 2 is running 647 00:43:58,275 --> 00:44:02,512 in this direction, so I go down in potential. 648 00:44:02,512 --> 00:44:09,157 So I get minus I 2 times R 3. But current I 1 is coming 649 00:44:09,157 --> 00:44:12,215 towards me. [inaudible] if I go in this 650 00:44:12,215 --> 00:44:17,287 direction, I 1 is coming towards me, so I climb up the potential 651 00:44:17,287 --> 00:44:19,943 hill. So I got plus I 1 times R 3. 652 00:44:19,943 --> 00:44:24,612 Now I go through R 3 in this direction, current I 2 is also 653 00:44:24,612 --> 00:44:28,476 in this direction, and so this must have a higher 654 00:44:28,476 --> 00:44:32,501 potential that this, so I go downhill in potential, 655 00:44:32,501 --> 00:44:36,768 so I have minus I 2 times R 2. I come down here -- ah, 656 00:44:36,768 --> 00:44:41,572 here's a battery. And it goes up in potential. 657 00:44:41,572 --> 00:44:44,278 So I get plus V 2, and that's zero. 658 00:44:44,278 --> 00:44:46,745 Two equations with two unknowns. 659 00:44:46,745 --> 00:44:50,247 I can solve for I 1, and I can solve for I 2. 660 00:44:50,247 --> 00:44:54,067 So I 1 and I 2 pop out. Let us assume that I 1 is 661 00:44:54,067 --> 00:44:56,694 positive, I find a positive value. 662 00:44:56,694 --> 00:44:59,797 It means, it's really in this direction. 663 00:44:59,797 --> 00:45:02,503 Let's suppose that I 1 is negative. 664 00:45:02,503 --> 00:45:06,96 I find minus three amperes. Well, it means that I 1 is in 665 00:45:06,96 --> 00:45:10,382 this direction, big deal. 666 00:45:10,382 --> 00:45:15,036 And so the whole operation is sign sensitive. 667 00:45:15,036 --> 00:45:20,006 And the same is true here. If I two is positive, 668 00:45:20,006 --> 00:45:23,284 it means it's in this direction. 669 00:45:23,284 --> 00:45:28,255 If I 2 is negative, then it's in that direction. 670 00:45:28,255 --> 00:45:33,437 How about I 3 now? Well, let us assume that I 1 is 671 00:45:33,437 --> 00:45:38,513 plus three amperes, and that you find that I 2 is 672 00:45:38,513 --> 00:45:42,995 plus one ampere. That's possible, 673 00:45:42,995 --> 00:45:45,559 right? You have two equations, 674 00:45:45,559 --> 00:45:49,009 two unknowns, and these are the answers. 675 00:45:49,009 --> 00:45:53,254 So three amperes goes like this [wssshhht], down, 676 00:45:53,254 --> 00:45:56,88 and one ampere comes up. Well, it's clear, 677 00:45:56,88 --> 00:46:00,948 then, that I 3 is three minus one, is plus two. 678 00:46:00,948 --> 00:46:05,901 Another way of looking at it is, three amperes come in at 679 00:46:05,901 --> 00:46:08,731 this juncture, I 2 is one ampere, 680 00:46:08,731 --> 00:46:13,153 so one ampere goes through, so two 681 00:46:13,153 --> 00:46:16,882 must go down. That's really Kirchoff's second 682 00:46:16,882 --> 00:46:19,678 rule. If I 1 were plus one ampere, 683 00:46:19,678 --> 00:46:24,339 and I 2 was also plus one ampere, then I 3 will be zero. 684 00:46:24,339 --> 03. No current would flow through I 685 03. --> 00:46:27,135 But my method would still work. 686 00:46:27,135 --> 00:46:32,219 But my method would still work. I find one ampere going down, 687 00:46:32,219 --> 00:46:36,54 and one ampere going up, so there's no -- no current 688 00:46:36,54 --> 00:46:41,963 going through R th- there's only current going in this direction, 689 00:46:41,963 --> 00:46:45,437 one ampere. And so, you have to recognize, 690 00:46:45,437 --> 00:46:49,59 then, that I 3 is I 1 minus I 2, 691 00:46:49,59 --> 00:46:52,766 which is really application, then, of Kirchoff's second 692 00:46:52,766 --> 00:46:54,06 rule. I like this idea, 693 00:46:54,06 --> 00:46:57,237 of a closed loop current, I know that some of you don't 694 00:46:57,237 --> 00:47:00,119 like it, that's fine. The reason why I like it is, 695 00:47:00,119 --> 00:47:02,002 I g- always end up, in this case, 696 00:47:02,002 --> 00:47:05,12 with two equations with two unknowns, I solve for I 1, 697 00:47:05,12 --> 00:47:07,708 I solve for I 2, and then the third one comes 698 00:47:07,708 --> 00:47:10,061 out in natural way by just thinking, "Ah! 699 00:47:10,061 --> 00:47:13,297 One current goes in this direction and the other goes in 700 00:47:13,297 --> 00:47:16,709 that direction." But if you prefer the method that the book 701 00:47:16,709 --> 00:47:19,532 will present to you, you get three equations with 702 00:47:19,532 --> 00:47:23,47 three unknowns, and you get I 1, 703 00:47:23,47 --> 00:47:26,29 I 2, and I 3, right at the start, 704 00:47:26,29 --> 00:47:30,342 you get an I 3. You see, I don't even start off 705 00:47:30,342 --> 00:47:34,395 with an I 3, it's not there, it comes in later. 706 00:47:34,395 --> 00:47:39,153 So the choice is yours. Now I want to entertain you for 707 00:47:39,153 --> 00:47:42,941 the last six minutes with something amazing, 708 00:47:42,941 --> 00:47:45,672 something that is truly amazing. 709 00:47:45,672 --> 00:47:50,166 And it is a form of a battery that is mind-boggling. 710 00:47:50,166 --> 00:47:55,811 And the battery is right here, on my -- my left, 711 00:47:55,811 --> 00:47:59,84 on your right. It is a battery that produces 712 00:47:59,84 --> 00:48:03,307 an enormous potential difference, ten, 713 00:48:03,307 --> 00:48:07,992 twenty kilovolts -- you see a schematic here on the 714 00:48:07,992 --> 00:48:11,74 transparency, you have a bucket of water, 715 00:48:11,74 --> 00:48:15,675 unintelligible the top, and you have glass, 716 00:48:15,675 --> 00:48:20,922 and the bucket of water is hiding behind here -- it's not 717 00:48:20,922 --> 00:48:26,731 that because we hide it from you, but that's the 718 00:48:26,731 --> 00:48:30,994 best place to be -- and you see plastic tubing coming down, 719 00:48:30,994 --> 00:48:35,403 and the water can run out on the right, and it can run out on 720 00:48:35,403 --> 00:48:37,314 the left. It runs out here, 721 00:48:37,314 --> 00:48:41,282 there is a, uh -- some paint can, no top and no bottom. 722 00:48:41,282 --> 00:48:45,177 And you see this paint can here, it's completely open. 723 00:48:45,177 --> 00:48:48,704 There's a letter A. And there's another paint can 724 00:48:48,704 --> 00:48:51,056 on the right, there's a letter B. 725 00:48:51,056 --> 00:48:54,804 It's a conducting can. And this is also a conducting 726 00:48:54,804 --> 00:48:56,861 can. And this water runs into 727 00:48:56,861 --> 00:49:03,616 another conducting trash can, and this water also runs into a 728 00:49:03,616 --> 00:49:07,787 conducting trash can. And now comes the key point, 729 00:49:07,787 --> 00:49:12,044 that this conductor here, A, is connected through a 730 00:49:12,044 --> 00:49:15,705 conducting wire with C, and the conductor B, 731 00:49:15,705 --> 00:49:19,451 the paint can, is connected with a conducting 732 00:49:19,451 --> 00:49:23,877 wire to this trash can D. You let the water run for a 733 00:49:23,877 --> 00:49:28,475 while, and you will see, between there two points here, 734 00:49:28,475 --> 00:49:32,303 sparks. Even when the points are as far 735 00:49:32,303 --> 00:49:34,343 apart as, say, five millimeters, 736 00:49:34,343 --> 00:49:38,227 when you're talking about at least a potential difference of 737 00:49:38,227 --> 00:49:40,991 something like ten, fifteen thousand volts, 738 00:49:40,991 --> 00:49:43,031 [poit], you will see the sparks. 739 00:49:43,031 --> 00:49:45,072 And you wait, see another spark. 740 00:49:45,072 --> 00:49:47,639 And you wait, and you see another spark. 741 00:49:47,639 --> 00:49:51,324 So this is a power supply. And that must be energy coming 742 00:49:51,324 --> 00:49:53,957 from somewhere. And so, problem four one, 743 00:49:53,957 --> 00:49:57,775 which you haven't seen yet, only unintelligible assignment, 744 00:49:57,775 --> 00:50:02,909 is asking you how this works. I will demonstrate it today, 745 00:50:02,909 --> 00:50:05,316 and I will come back to it later. 746 00:50:05,316 --> 00:50:08,401 The way it works is actually quite subtle, 747 00:50:08,401 --> 00:50:10,809 but I want you to think about it. 748 00:50:10,809 --> 00:50:14,721 It's a remarkable battery, a remarkable power supply. 749 00:50:14,721 --> 00:50:19,01 As the water starts running, I want to draw your attention 750 00:50:19,01 --> 00:50:23,449 to the fact that you can almost anticipate when the start -- 751 00:50:23,449 --> 00:50:26,459 when the spark occurs, because the water, 752 00:50:26,459 --> 00:50:29,468 at the very last, is beginning to spread. 753 00:50:29,468 --> 00:50:35,47 It doesn't come out any more, just like a narrow cylinder, 754 00:50:35,47 --> 00:50:39,917 but it begins to spread. And then comes the spark. 755 00:50:39,917 --> 00:50:43,637 And then it goes back to running normally, 756 00:50:43,637 --> 00:50:47,267 and then slowly, in time, it will spread, 757 00:50:47,267 --> 00:50:51,623 and then comes the spark. So let us get it going, 758 00:50:51,623 --> 00:50:56,25 have some light here, Marcos and Bill spent a lot of 759 00:50:56,25 --> 00:51:01,151 time getting this going -- Marcos, do we have -- are my 760 00:51:01,151 --> 00:51:07,04 lights the way you want them? You're happy with that. 761 00:51:07,04 --> 00:51:11,791 There, you see the two bowls, which are really here and 762 00:51:11,791 --> 00:51:16,63 let's first look at the sparks, so I will start the water 763 00:51:16,63 --> 0. running now. 764 0. --> 00:51:17,753 765 00:51:17,753 --> 00:51:20,69 Let's just be patient a little bit. 766 00:51:20,69 --> 00:51:23,628 And let's see unintelligible spark. 767 00:51:23,628 --> 00:51:25,96 Keep -- ah! Did you see one? 768 00:51:25,96 --> 00:51:30,021 Did you see the spark? Oh, you were not looking. 769 00:51:30,021 --> 00:51:33,218 Man, I'm paying for this. Look at the, 770 00:51:33,218 --> 00:51:38,063 uh, look at the two bowls. 771 00:51:38,063 --> 00:51:41,66 Give it some time again. I have to charge up. 772 00:51:41,66 --> 00:51:45,257 Oh, I can already anticipate, it's coming up, 773 00:51:45,257 --> 00:51:46,81 it's coming up, dah! 774 00:51:46,81 --> 00:51:50,325 Did you see it? Ten, fifteen thousand volts. 775 00:51:50,325 --> 00:51:55,475 Let's give it a little bit more time, and then we'll take a look 776 00:51:55,475 --> 00:51:58,254 at the water flow, which I can see, 777 00:51:58,254 --> 00:52:02,26 I'm close, but we can make you see the water flow. 778 00:52:02,26 --> 00:52:06,266 Look again. Ah, it's coming up -- 779 00:52:06,266 --> 00:52:08,053 ah! Did you see? 780 00:52:08,053 --> 00:52:14,727 I could see it coming up. I can make you listen by having 781 00:52:14,727 --> 00:52:21,4 my microphone near the water, and you can hear this water 782 00:52:21,4 --> 00:52:26,405 running, unintelligible sound to all of us. 783 00:52:26,405 --> 00:52:31,53 And now, the sound changes, you hear change? 784 00:52:31,53 --> 00:52:35,343 And there's the spark! Once more. 785 00:52:35,343 --> 00:52:42,016 It's running, spreading, coming up! 786 00:52:42,016 --> 00:52:43,563 Yah! Amazing, isn't it? 787 00:52:43,563 --> 00:52:46,797 I can make you see this water. Just stay there, 788 00:52:46,797 --> 00:52:49,258 we have one and a half minutes left. 789 00:52:49,258 --> 00:52:53,055 So now you can see the water. You happy with the light, 790 00:52:53,055 --> 00:52:55,094 Marcos? You can improve on it. 791 00:52:55,094 --> 00:52:56,781 So look at the water. Ah! 792 00:52:56,781 --> 00:53:01,07 It was just spreading already, you can't see the spark and the 793 00:53:01,07 --> 00:53:04,445 water at the same time. See, the water's running, 794 00:53:04,445 --> 00:53:07,539 now, normally? It's going to spread slowly -- 795 00:53:07,539 --> 00:53:13,233 I will tell you when I see the spark here, but it's already -- 796 00:53:13,233 --> 00:53:15,728 I can almost predict when it happens. 797 00:53:15,728 --> 00:53:19,401 The water is spreading now , coming up shortly -- yah! 798 00:53:19,401 --> 00:53:23,005 unintelligible the spark. And you immediately see the 799 00:53:23,005 --> 00:53:26,262 water go like this. I want you to think about it 800 00:53:26,262 --> 00:53:29,034 and explain this. This is one of the most 801 00:53:29,034 --> 53:34 remarkable things I've ever seen in my life.