1 00:00:02,300 --> 00:00:04,880 Welcome back to our course on linear circuits where today we're going to be 2 00:00:04,880 --> 00:00:09,780 talking about inductance. To, in this class we're going to be 3 00:00:09,780 --> 00:00:13,190 introducing a little bit about inductors and how they work. 4 00:00:13,190 --> 00:00:15,740 And we're going to calculate current and voltage in inductors. 5 00:00:15,740 --> 00:00:20,820 And as part of this, we'll also be discussing magnetic fields and how 6 00:00:20,820 --> 00:00:23,395 electricity and magnetism relate with one another. 7 00:00:23,395 --> 00:00:29,900 So, from a previous class we talked about capacitance, capacitors, and, we're able 8 00:00:29,900 --> 00:00:33,260 to do some derivations. The slide's that we're presenting now, 9 00:00:33,260 --> 00:00:36,288 this is inductance, then the next one will be inductors. 10 00:00:36,288 --> 00:00:41,460 And they are established in a very parrallell way to what the capacitence 11 00:00:41,460 --> 00:00:48,350 and capacitors were. The objectives of this lesson are to 12 00:00:48,350 --> 00:00:51,440 allow you to describe the construction and behavior of an inductor. 13 00:00:51,440 --> 00:00:55,230 And find the current through an inductor, as well as the voltage across an 14 00:00:55,230 --> 00:00:57,630 inductor. And then explain how you can get a 15 00:00:57,630 --> 00:00:59,620 voltage created at the cross of the conductor. 16 00:01:00,870 --> 00:01:05,300 So first off what are inductors? This is the first time that we actually 17 00:01:05,300 --> 00:01:09,820 need to know something about magnetism and in respect circuits that we are 18 00:01:09,820 --> 00:01:12,000 analyzing and it's going to start playing a role. 19 00:01:12,000 --> 00:01:18,090 What you essentially do is you have a current, coming from a current source 20 00:01:18,090 --> 00:01:25,250 that goes through a wire that is put in a particular geometric configuration. 21 00:01:25,250 --> 00:01:32,449 And when you do that, you get a magnetic field within this wire. 22 00:01:34,120 --> 00:01:38,770 And so just like an electric field in a capacitor stored up energy, you get a 23 00:01:38,770 --> 00:01:41,160 magnetic field and an inductor that stores up energy. 24 00:01:41,160 --> 00:01:46,140 And it establishes some current going through your inductor. 25 00:01:46,140 --> 00:01:49,290 Which you can then attach to some other device. 26 00:01:49,290 --> 00:01:53,360 And this current is going to keep trying to push through the device. 27 00:01:55,960 --> 00:01:59,062 And so we're going to kind of see how all of these things work together. 28 00:01:59,062 --> 00:02:04,398 today. So, where we presented before with 29 00:02:04,398 --> 00:02:09,130 capacitance, how currents and voltage is related, we are going to do the same 30 00:02:09,130 --> 00:02:11,912 thing with inductors. One of the things about inductors is 31 00:02:11,912 --> 00:02:16,300 they're sometimes drawn slightly differently, depending upon what you're 32 00:02:16,300 --> 00:02:19,665 looking at. So both of these are examples of how 33 00:02:19,665 --> 00:02:22,370 inductors are sometimes drawn. All of them kind of looks like this where 34 00:02:22,370 --> 00:02:27,260 they have bumps or curls. And what that is essentially showing is 35 00:02:27,260 --> 00:02:29,540 the curls of the wires that are being placed. 36 00:02:29,540 --> 00:02:32,180 And we'll talk a little more about that when we speak about the physical 37 00:02:32,180 --> 00:02:36,630 construction of inductors. The voltage in an inductor is equal to L 38 00:02:36,630 --> 00:02:42,600 times the didt where L is an inductance. Inductance is a unit that's measured in 39 00:02:42,600 --> 00:02:46,240 henry's. We are going to use L in our calculations 40 00:02:46,240 --> 00:02:50,700 to reference it and like when we are talking about capacitance referring to 41 00:02:50,700 --> 00:02:53,450 how well a material is holding an electric field. 42 00:02:53,450 --> 00:02:55,800 This relates to how well it's holding a magnetic field. 43 00:02:56,860 --> 00:03:00,206 And then again, if you want to invert that operation and find the current, then 44 00:03:00,206 --> 00:03:03,080 it's 1 over L. And then you're integrating the voltage 45 00:03:03,080 --> 00:03:08,770 with respect to time. To understand how these inductors are 46 00:03:08,770 --> 00:03:12,165 actually working behaviorally though, we need to know something about this 47 00:03:12,165 --> 00:03:14,998 electromagnetism that I mentioned. And so we're going to learn about 48 00:03:14,998 --> 00:03:18,045 Ampere's Law. Ampere's Law states that if I have a 49 00:03:18,045 --> 00:03:26,967 current moving through a material, that moving charge generates the magnetic 50 00:03:26,967 --> 00:03:29,260 field. And the magnetic field is going to be 51 00:03:29,260 --> 00:03:34,306 generated in a ring around your wire like this. 52 00:03:34,306 --> 00:03:37,270 And the way you can tell the direction is by using what's called the right hand 53 00:03:37,270 --> 00:03:40,770 rule. So, this dot could be seen as current 54 00:03:40,770 --> 00:03:46,420 coming out of the page. So if you point your thumb out of a page, 55 00:03:47,990 --> 00:03:51,770 and this is your right thumb, mind you, because it's the right hand rule. 56 00:03:52,890 --> 00:03:56,420 Then the curves of these arrows arrows are going to match the curves of your 57 00:03:56,420 --> 00:03:58,260 fingers. The direction that your fingers are 58 00:03:58,260 --> 00:04:01,070 pointing. So, that's how you can identify the 59 00:04:01,070 --> 00:04:06,230 direction. And these lines represent magnetic fields 60 00:04:06,230 --> 00:04:09,790 of a particular strength. Magnetic fields drop off the same way 61 00:04:09,790 --> 00:04:14,480 that electric fields kind of do, with this inverse square type of a property. 62 00:04:14,480 --> 00:04:18,150 So, as you move further and further away, the magnetic field is going to become 63 00:04:18,150 --> 00:04:20,170 weaker and weaker. And it's going to happen very drastically 64 00:04:20,170 --> 00:04:23,320 and very quickly. So, how do we actually use this to do 65 00:04:23,320 --> 00:04:26,905 something with a device? Well this is how we construct an 66 00:04:26,905 --> 00:04:31,720 inductor. Here this kind of a bluish gray material, 67 00:04:34,420 --> 00:04:37,730 is a ferrous core. Now for an inductor it doesn't need to be 68 00:04:37,730 --> 00:04:39,610 there, but it makes the inductor work better. 69 00:04:39,610 --> 00:04:42,970 And we'll see exactly what that means, here, shortly. 70 00:04:42,970 --> 00:04:45,020 And then we have a wire here that's going to wrap around. 71 00:04:46,070 --> 00:04:50,800 Now if you see an actual inductor, you'll see something that looks like it's just 72 00:04:50,800 --> 00:04:56,142 bare wire that's wrapped around. its usually just a copper color sometime 73 00:04:56,142 --> 00:04:59,534 it's just reddish it's not actually bare wire, it is insulated. 74 00:04:59,534 --> 00:05:03,246 But with thin insulation so this wire is normally called a magnet wire. 75 00:05:03,246 --> 00:05:07,406 And that's why I've colored it this kind of reddish to look some what like the 76 00:05:07,406 --> 00:05:09,838 magnet wire that you'd see on a real inductor. 77 00:05:09,838 --> 00:05:13,530 And then here, i represents the currents flowing through the wire. 78 00:05:13,530 --> 00:05:16,390 To see how this device is working, what we're going to do is take a cross section 79 00:05:16,390 --> 00:05:22,380 of this. Here, all of these dots represent current 80 00:05:22,380 --> 00:05:26,170 coming out of the page. And all of these x's represent current 81 00:05:26,170 --> 00:05:30,490 going into the page. As you send this current through, it 82 00:05:30,490 --> 00:05:34,330 establishes a magnetic field. And here we can see kind of a shape of 83 00:05:34,330 --> 00:05:37,180 what that magnetic field looks like. And the way that that's established is, 84 00:05:38,220 --> 00:05:43,400 each of these wires is generating magnetic field going around in circles 85 00:05:43,400 --> 00:05:45,770 like this. And since all of these are placed side by 86 00:05:45,770 --> 00:05:51,579 side, this one is also making a magnetic field as playing around like this and 87 00:05:51,579 --> 00:05:55,110 this one is pointing like this. So, start with what happens is it 88 00:05:55,110 --> 00:05:59,660 establishes a magnetic field here that's almost like parallel lines. 89 00:05:59,660 --> 00:06:04,400 Because its from this combination of all these individual magnetic fields. 90 00:06:04,400 --> 00:06:09,680 If you look at the other side as it's going into the page, they have the same 91 00:06:09,680 --> 00:06:12,400 looping structure. But now, thanks to the right hand law, we 92 00:06:12,400 --> 00:06:16,610 see that these arrows are going to point like this. 93 00:06:16,610 --> 00:06:19,090 So here, they're going clockwise, here, they're going counterclockwise. 94 00:06:19,090 --> 00:06:23,110 But if you'll notice, in the middle, all these arrows point the same direction. 95 00:06:23,110 --> 00:06:27,638 So, both sides of the coil are pushing magnetic field in the same direction. 96 00:06:27,638 --> 00:06:36,790 Now our capacitance or our inductance, rather is letting us know how well this 97 00:06:36,790 --> 00:06:41,850 core holds a magnetic field. And so often times you use a ferrous cord 98 00:06:41,850 --> 00:06:47,170 or ferrous meaning it has iron in it. Because things that have iron in it hold 99 00:06:47,170 --> 00:06:50,690 magnetic fields better. And perceptually what it means is that as 100 00:06:50,690 --> 00:06:56,540 your inductance gets larger, this magnetic field is going to make the 101 00:06:56,540 --> 00:07:00,185 current want to keep pushing through. Kind of in a constant rate. 102 00:07:00,185 --> 00:07:06,899 So now we'll start looking a little bit more at the implications of that. 103 00:07:09,390 --> 00:07:13,630 We've talked about wires and how we have no potential difference across wires. 104 00:07:13,630 --> 00:07:17,105 So [UNKNOWN] potential. Because voltages are created by 105 00:07:17,105 --> 00:07:20,750 differences in charge density, and if it's a wire then the charge is able to 106 00:07:20,750 --> 00:07:24,050 freely move And make its way around through the 107 00:07:24,050 --> 00:07:28,530 material until it is evenly distributed. So we don't see voltages across wires. 108 00:07:28,530 --> 00:07:33,180 But we do across an inductor, even though an inductor is essentially just a wrap of 109 00:07:33,180 --> 00:07:35,520 wire. And the reason we see this is because of 110 00:07:35,520 --> 00:07:37,820 magnetic fields that are being established. 111 00:07:37,820 --> 00:07:40,970 So to better understand how that works, suppose I have a current source here. 112 00:07:40,970 --> 00:07:45,440 It's been hooked up to this inductor for a little while and so there's a magnetic 113 00:07:45,440 --> 00:07:49,450 field. Here represented by these two red curves 114 00:07:49,450 --> 00:07:54,869 in this inductor. Now suppose I increase my current. 115 00:07:54,869 --> 00:07:58,770 Well, the thing about conductors is they want to keep their current flowing at a 116 00:07:58,770 --> 00:08:02,370 nice steady pace. And if you try and change the current 117 00:08:02,370 --> 00:08:08,590 flow, then things start to get backed up. So we start letting extra charge flow out 118 00:08:08,590 --> 00:08:13,120 of this source. But as it does that, this charge is going 119 00:08:13,120 --> 00:08:15,820 too quickly. It's going more quickly than this 120 00:08:15,820 --> 00:08:18,312 inductor has established that current should flow. 121 00:08:18,312 --> 00:08:24,410 So, these extra charges here on this end have to kind of wait their turn. 122 00:08:24,410 --> 00:08:29,730 And they kind of group up a little bit. But just like the charges were pushing in 123 00:08:29,730 --> 00:08:35,540 capacitors, that kind of behavior. This source still wants to pull charge 124 00:08:35,540 --> 00:08:45,010 carriers from here and as it does that we see we get a positive collection of 125 00:08:45,010 --> 00:08:47,800 charge. These are all atoms that have lost some 126 00:08:47,800 --> 00:08:50,255 of their electrons they give a positive charge on this side. 127 00:08:50,255 --> 00:08:54,100 And so what ends up happening? Well, now we can see that there starts to 128 00:08:54,100 --> 00:08:57,190 be established this difference in charge density. 129 00:08:57,190 --> 00:09:01,350 And so now there is a voltage, even though it's through a wire by the charge 130 00:09:01,350 --> 00:09:04,425 kind of getting grouped up. If we did it the other way, and we 131 00:09:04,425 --> 00:09:07,590 decreased the current on this source. [INAUDIBLE]. 132 00:09:07,590 --> 00:09:10,050 The same thing would basically happen, but opposite. 133 00:09:10,050 --> 00:09:14,900 This inductor would be pushing current through faster than the source was 134 00:09:14,900 --> 00:09:18,170 accepting it. So in this case, you're going to then see 135 00:09:18,170 --> 00:09:26,239 electrons grouping up on this side. And then positive ions on this side. 136 00:09:30,580 --> 00:09:33,770 So to summarize what we presented today. We talked about the equations for current 137 00:09:33,770 --> 00:09:37,000 and voltage in inductors. We talked about Ampere's Law, that shows 138 00:09:37,000 --> 00:09:39,910 how the flow of current gives us magnetic fields. 139 00:09:39,910 --> 00:09:43,710 Showing one way that electricity and magnetism interrelate. 140 00:09:43,710 --> 00:09:47,470 And then we showed how voltage can be created across an inductor, even though 141 00:09:47,470 --> 00:09:51,240 it's technically only a wire. Now, some of the things about these 142 00:09:51,240 --> 00:09:54,520 magnetic fields, might be something very new to you. 143 00:09:54,520 --> 00:09:56,890 So, if you have questions about the magnetic fields, and how these things are 144 00:09:56,890 --> 00:09:59,190 operating. go to the forums and post your questions 145 00:09:59,190 --> 00:10:01,520 there, so that we can make sure that you're understanding the material that's 146 00:10:01,520 --> 00:10:04,415 being presented here. In our next class, we'll present 147 00:10:04,415 --> 00:10:08,850 inductors as actual circuit elements, and see how they interact in a circuit 148 00:10:08,850 --> 00:10:10,520 environment. Until next time.