1 00:00:00,025 --> 00:00:07,920 Hello, I'm Nathan Parrish and this Linear Circuits. 2 00:00:07,920 --> 00:00:11,592 We're going to be looking at some basic linear circuits and some of the devices 3 00:00:11,592 --> 00:00:15,102 that use linear circuits, to give a quick introduction to some of the basics in 4 00:00:15,102 --> 00:00:21,830 electrical engineering. We're going to be starting with looking 5 00:00:21,830 --> 00:00:25,610 at current and charge, and the aims of this particular lesson are to help you 6 00:00:25,610 --> 00:00:29,450 calculate the forces that charges exert on one another, and to calculate the 7 00:00:29,450 --> 00:00:35,292 functions of current and charge. Now you might remember from the previous 8 00:00:35,292 --> 00:00:38,556 class, that there was a different person who was presenting, that was Doctor 9 00:00:38,556 --> 00:00:43,273 Ferri, and we teach this class together. As part of that, she introduced the 10 00:00:43,273 --> 00:00:47,149 course as a broad outline, as well as she covered the basic overview of module one, 11 00:00:47,149 --> 00:00:50,968 which is the background module, giving you the, the bare essentials that we will 12 00:00:50,968 --> 00:00:57,670 need before we can start talking about more interesting things. 13 00:00:57,670 --> 00:01:00,842 To put these topics in context with the rest of the module, we will start by 14 00:01:00,842 --> 00:01:05,312 talking about charge and current. And after we've talked about these 15 00:01:05,312 --> 00:01:08,432 things, we can then start talking about things like voltage, and power, and at 16 00:01:08,432 --> 00:01:11,264 the end of this module we will even introduce you to some basic electric 17 00:01:11,264 --> 00:01:15,510 circuits, so that we can start doing some analysis. 18 00:01:16,890 --> 00:01:20,300 The objectives of this lesson are, to first of all, help you to identify the 19 00:01:20,300 --> 00:01:23,820 forces that charges exert on one another, and then to allow you to calculate a 20 00:01:23,820 --> 00:01:28,990 charge, based upon a current, and a current based upon a charge. 21 00:01:30,700 --> 00:01:34,544 In talking about charge, charge is, a fundamental property of matter, all 22 00:01:34,544 --> 00:01:38,630 matter has charge. And it comes in quantized, discrete 23 00:01:38,630 --> 00:01:42,507 amounts. This amount is known as the fundamental 24 00:01:42,507 --> 00:01:48,760 charge, and it is equal to 1.602 times 10 to the negative 19th Coulombs. 25 00:01:48,760 --> 00:01:52,216 All protons have one positive elementary charge, and all electrons have one 26 00:01:52,216 --> 00:01:56,184 negative elementary charge. You might also remember about neutrons 27 00:01:56,184 --> 00:01:59,470 from basic physics, where neutrons have neutral charge. 28 00:02:00,610 --> 00:02:03,452 Electromagnetism is a fundamental property of matter, and you might 29 00:02:03,452 --> 00:02:07,980 remember that all the protons are held together in the nucleus. 30 00:02:07,980 --> 00:02:11,180 And why is it that they aren't just, pushed apart? 31 00:02:11,180 --> 00:02:13,690 Well, it turns out that there's other forces that work here. 32 00:02:13,690 --> 00:02:17,082 The electric strong force holds the protons together in the nucleus and it's 33 00:02:17,082 --> 00:02:21,469 about 137 times more. Strong than electromagnetic force, but on 34 00:02:21,469 --> 00:02:26,092 the other hand, electromagnetic force is about 36 orders of magnitude stronger 35 00:02:26,092 --> 00:02:30,448 than gravitation. Which means that if you held your cell 36 00:02:30,448 --> 00:02:32,880 phone upside down, it's going to work equally as well as holding it right side 37 00:02:32,880 --> 00:02:35,925 up. When we talk about charge we're measuring 38 00:02:35,925 --> 00:02:39,869 it in units of Coulombs, after Charles Augustine Coulomb, an 18th century French 39 00:02:39,869 --> 00:02:43,945 physicist. And when we represent Coulombs, we're 40 00:02:43,945 --> 00:02:49,298 going to use a capital C. When we use these values in equations, 41 00:02:49,298 --> 00:02:52,532 we're going to use a q, sometimes it's a lowercase q and sometimes it's a capital 42 00:02:52,532 --> 00:02:55,514 Q. It doesn't particularly matter which we 43 00:02:55,514 --> 00:02:59,035 use just so long as the, you know, that q reference is charge. 44 00:02:59,035 --> 00:03:03,323 The electromagnetic force that is exerted on particles can be calculated using 45 00:03:03,323 --> 00:03:08,238 something called Coulomb's Law. Coulomb's Law states that the strength of 46 00:03:08,238 --> 00:03:11,718 the force that charges exert on one another is equal to k sub b times the 47 00:03:11,718 --> 00:03:16,590 quantity q one times q two, divided by r squared. 48 00:03:16,590 --> 00:03:19,194 Here q one is the charge of the first particle, q two the charge of the second 49 00:03:19,194 --> 00:03:23,170 particle. And r is the distance between them. 50 00:03:23,170 --> 00:03:27,462 K sub e is Coulomb's constant. It's a fundamental constant of nature, 51 00:03:27,462 --> 00:03:31,660 and that is equal to 1 over 4 pi epsilon naught. 52 00:03:31,660 --> 00:03:35,170 And it is in units of Newtons meter squared per Coulomb squared. 53 00:03:35,170 --> 00:03:38,159 Here, the pi is the pi that you're familiar with from basic math, 3.14159, 54 00:03:38,159 --> 00:03:41,695 and so on. Epsilon naught is known as the 55 00:03:41,695 --> 00:03:44,196 permittivity of free space, which is something that you're probably not 56 00:03:44,196 --> 00:03:46,394 familiar with. And we'll talk about it more in the 57 00:03:46,394 --> 00:03:48,766 future. But again, this is a constant property of 58 00:03:48,766 --> 00:03:51,816 matter. If you put them all together, k sub b is 59 00:03:51,816 --> 00:03:56,528 approximately equal to 8.988 times 10 to the 9th Newtons Meter squared per 60 00:03:56,528 --> 00:04:00,856 Coloumbs squared. The way that these charges interact with 61 00:04:00,856 --> 00:04:03,110 each other is through something called an electric field. 62 00:04:03,110 --> 00:04:07,170 If we look at electric fields, positive charge is going to have an electric field 63 00:04:07,170 --> 00:04:10,660 that pushes outward radially in this manner. 64 00:04:10,660 --> 00:04:13,696 We use the arrows to distinguish the direction that other positive charges are 65 00:04:13,696 --> 00:04:16,717 going to be pushed. If we look in turn at a negative charge, 66 00:04:16,717 --> 00:04:19,523 it's going to have the same basic behavior, but the arrows point the other 67 00:04:19,523 --> 00:04:22,880 way. Because it's going to attract positive 68 00:04:22,880 --> 00:04:25,870 charge inward towards itself. Now neither of these is particularly 69 00:04:25,870 --> 00:04:28,670 interesting, but if we start putting them together, that's when things start to get 70 00:04:28,670 --> 00:04:32,741 a little bit more interesting. And, the most common configuration for 71 00:04:32,741 --> 00:04:35,415 doing this is in something called an electric dipole. 72 00:04:35,415 --> 00:04:38,535 This is where we take a positive charge and a negative charge, put them in close 73 00:04:38,535 --> 00:04:43,078 proximity and fix them. And when we look at this we get kind of 74 00:04:43,078 --> 00:04:48,628 an interesting field behavior. So here, if we have a positive charge and 75 00:04:48,628 --> 00:04:51,526 a negative charge here, and we place a positive charge somewhere in between 76 00:04:51,526 --> 00:04:54,700 them, the charge is going to be basically pushed straight from the positive, here, 77 00:04:54,700 --> 00:04:59,295 to the negative, here. But it gets a little more interesting if 78 00:04:59,295 --> 00:05:03,380 we put perhaps the positive charge somewhere out here. 79 00:05:03,380 --> 00:05:06,500 Because it's so close to the positive charge, it's going to be basically 80 00:05:06,500 --> 00:05:10,909 trending away from this positive charge. But just because the negative charge is 81 00:05:10,909 --> 00:05:13,280 further away, it doesn't mean it has no effect. 82 00:05:13,280 --> 00:05:16,920 It will have an effect and will start to try and pull it towards it, which causes 83 00:05:16,920 --> 00:05:20,672 this positive charge to be pushed, as it goes outward, slightly over and curving 84 00:05:20,672 --> 00:05:24,435 around. And so it's the interaction between the 85 00:05:24,435 --> 00:05:27,460 positive and the negative that cause this curving behavior. 86 00:05:31,420 --> 00:05:33,630 Now that we know something of electric fields, this allows us to start talking 87 00:05:33,630 --> 00:05:36,097 about current. The way that we define current is by 88 00:05:36,097 --> 00:05:39,470 looking at a material we come up with a cross-sectional area. 89 00:05:39,470 --> 00:05:42,753 And then we count the amount of charge that passes through that cross-sectional 90 00:05:42,753 --> 00:05:46,615 area in a given period of time. But, we would like to know what the 91 00:05:46,615 --> 00:05:50,868 current is at an instant of time. The way that we do that is we take these, 92 00:05:50,868 --> 00:05:55,605 slices of time and make them smaller and smaller, until they approach zero. 93 00:05:55,605 --> 00:05:58,165 You might remember from calculus that what we're essentially doing here is, 94 00:05:58,165 --> 00:06:01,850 we're taking it the limit. And so when we do that, we take the ratio 95 00:06:01,850 --> 00:06:04,650 of charge with respect to time. And take the limit as time becomes 96 00:06:04,650 --> 00:06:07,327 smaller and smaller. What we're essentially doing is taking 97 00:06:07,327 --> 00:06:10,560 the derivative. Hence to calculate the current. 98 00:06:10,560 --> 00:06:12,255 We take the time derivative of the charge. 99 00:06:12,255 --> 00:06:15,711 It becomes very simple then to invert this operation if we desire to know what 100 00:06:15,711 --> 00:06:20,020 the current is. What the charge based upon the current. 101 00:06:20,020 --> 00:06:23,530 We do this by simply integrating but to get a complete picture, we must also add 102 00:06:23,530 --> 00:06:27,930 the initial charge. Now we can measure this current in units 103 00:06:27,930 --> 00:06:32,955 of Coulombs per second, or we can use the unit of Amperes, or Amps, which is itself 104 00:06:32,955 --> 00:06:38,234 a unit. We designate it using an A, and Amperes 105 00:06:38,234 --> 00:06:41,996 are named after again, a French physicist, Andre-Marie Ampere, who was 106 00:06:41,996 --> 00:06:47,696 one of the first people to study current. When we do equations, we're going to be 107 00:06:47,696 --> 00:06:50,405 using the variable i to represent the flow of current. 108 00:06:50,405 --> 00:06:54,365 And the reason we use i, is because in his research, Andre-Marie Ampere used the 109 00:06:54,365 --> 00:06:58,400 term intensity of current. To represent this value. 110 00:06:58,400 --> 00:07:01,395 And so we use the i from intensity to represent the current. 111 00:07:01,395 --> 00:07:04,893 It becomes very important when we're doing these types of calculations to keep 112 00:07:04,893 --> 00:07:08,380 in mind what our reference directions happen to be. 113 00:07:08,380 --> 00:07:11,719 And this is one of the areas that most beginning electrical circuits and 114 00:07:11,719 --> 00:07:15,058 students really start to trip up is by not keeping the reference directions 115 00:07:15,058 --> 00:07:19,224 straight. So, to help you better understand, we're 116 00:07:19,224 --> 00:07:22,386 going to start by talking a little bit about electric charge. 117 00:07:22,386 --> 00:07:26,610 If we have a charge that's slowing, it's actually not generally the positive 118 00:07:26,610 --> 00:07:29,705 charge that's moving. It's the negative charge. 119 00:07:29,705 --> 00:07:33,649 And the reason for this is when Benjamin Franklin, an American, scientist was 120 00:07:33,649 --> 00:07:37,651 studying charge, he noticed that rubbing two materials together caused charge to 121 00:07:37,651 --> 00:07:42,776 be transferred from one to the other. And so he just made an assignment, made 122 00:07:42,776 --> 00:07:45,614 one positive and the other negative, it turns out that the negative ones are the 123 00:07:45,614 --> 00:07:49,688 ones that move. So to start looking at this in 124 00:07:49,688 --> 00:07:53,775 perspective, if we have one Amp of current flowing here, as labeled in the 125 00:07:53,775 --> 00:07:57,982 left diagram. What that means is that we have one 126 00:07:57,982 --> 00:08:03,120 Coulomb of charge, every second, flowing from the top to the bottom. 127 00:08:03,120 --> 00:08:07,472 But in practice it's actually negative one Coulomb of electrons pulling from the 128 00:08:07,472 --> 00:08:12,360 bottom to the top. If we look at this figure on the right 129 00:08:12,360 --> 00:08:16,952 it's basically saying the same thing. We've changed the current from positive 130 00:08:16,952 --> 00:08:20,095 to a negative and we've changed the arrow direction. 131 00:08:20,095 --> 00:08:24,197 But again, it's negative one Coulomb. Of charge going from the bottom to the 132 00:08:24,197 --> 00:08:27,812 top every second. And by keeping your reference structure 133 00:08:27,812 --> 00:08:30,779 straight it will make sure that you don't end up getting strange values when you're 134 00:08:30,779 --> 00:08:35,780 doing you're basic analysis calculations. In summary, we discussed charge as a 135 00:08:35,780 --> 00:08:39,010 property of matter. We discussed how we can calculate the 136 00:08:39,010 --> 00:08:43,740 forces the charges exert on one another. We were able to calculate current by 137 00:08:43,740 --> 00:08:47,380 taking the derivative of charge and calculate charge by taking an integral of 138 00:08:47,380 --> 00:08:51,740 the current with respect to time. We've also emphasized the importance of 139 00:08:51,740 --> 00:08:54,100 being straight with your reference directions when you're doing your 140 00:08:54,100 --> 00:08:58,220 calculations. So for my next class we're going to be 141 00:08:58,220 --> 00:09:02,440 taking a closer look at electric fields. We will present the idea of voltage, and 142 00:09:02,440 --> 00:09:05,740 then we'll actually have a practical example of seeing how voltage behaves, by 143 00:09:05,740 --> 00:09:10,472 looking at how a car battery works. I'll remind you that there are forums 144 00:09:10,472 --> 00:09:13,927 online where you can post your questions. Doctor Ferri and I are both going to be 145 00:09:13,927 --> 00:09:16,894 monitoring those forums. And you are encouraged to go and 146 00:09:16,894 --> 00:09:19,670 participate in the forums and answer other peoples' questions. 147 00:09:19,670 --> 00:09:22,500 It's a great way for you to learn by teaching others. 148 00:09:22,500 --> 00:09:25,110 And it should be an excellent opportunity for us to get together. 149 00:09:25,110 --> 00:09:27,898 That's actually the primary way of being able to, to ask questions of Doctor Ferri 150 00:09:27,898 --> 00:09:30,070 and me. So we look forward to seeing you on 151 00:09:30,070 --> 00:09:32,940 forums, and look forward to seeing you next time. 152 00:09:32,940 --> 00:09:33,600 'Til then, cheers.