1 00:00:00,012 --> 00:00:04,802 So, in this video, we're finally going to define voltage and current so we can 2 00:00:04,802 --> 00:00:09,049 begin to talk about electrical signals and how they behave. 3 00:00:09,049 --> 00:00:12,728 So, we'll define voltage and current. It's pretty easy. 4 00:00:12,728 --> 00:00:15,543 We're not going to use too much physics here. 5 00:00:15,543 --> 00:00:20,284 It's going to be very intuitive, I hope. We'll then talk about the circuit 6 00:00:20,284 --> 00:00:23,971 elements. These are elements that act on voltage 7 00:00:23,971 --> 00:00:29,676 and current in very particular ways and these are used to construct real-life 8 00:00:29,676 --> 00:00:33,559 analog circuits. So, what are voltage and current? So, 9 00:00:33,559 --> 00:00:39,617 voltage is also called electric potential and it provides the push for the flow of 10 00:00:39,617 --> 00:00:44,797 charged particles. So, the idea is that you have a region of 11 00:00:44,797 --> 00:00:51,842 positive to negative voltage and the positive part is suppose to represent 12 00:00:51,842 --> 00:00:58,442 that it has a higher potential, electricall potential than the negative 13 00:00:58,442 --> 00:01:01,682 side. So, this is downhill if you will. 14 00:01:01,682 --> 00:01:06,806 Higher potential where it's positive and lower potential where it's negative. 15 00:01:06,806 --> 00:01:11,404 And so generally, if you just had a charged particle, a positively charged 16 00:01:11,404 --> 00:01:16,534 particle, it would want to go down hill. That's what a voltage does, it provides 17 00:01:16,534 --> 00:01:19,022 the push. Voltage has units of volts. 18 00:01:19,022 --> 00:01:26,103 usually indicated for lowercase v, sometimes for uppercase V named for 19 00:01:26,103 --> 00:01:32,252 Allesandro Volta, the Italian who, this is history, discovered the battery 20 00:01:32,252 --> 00:01:36,949 [UNKNOWN]. Current is the flow of positevely charged 21 00:01:36,949 --> 00:01:40,872 particles in the direction that's indicated. 22 00:01:40,872 --> 00:01:47,552 So, what this means here is that there's a river of charged particles flowing this 23 00:01:47,552 --> 00:01:53,139 way and notice the word current, is analagous to the flow of water in a 24 00:01:53,139 --> 00:01:58,812 stream or river and the current is flowing this way. So, the interesting 25 00:01:58,812 --> 00:02:04,432 thing though is that this is the flow of the positively charged particles. 26 00:02:04,432 --> 00:02:10,392 If you had negatively charged particles like an electron flowing in this way, it 27 00:02:10,392 --> 00:02:16,267 turns out positive current to the right means the electrons are flowing to the 28 00:02:16,267 --> 00:02:19,749 left. you can blame this convention of getting 29 00:02:19,749 --> 00:02:24,451 negative charge assigned to an electron to Benjamin Franklin. 30 00:02:24,451 --> 00:02:30,588 as you probably know, it's the electron that's the workforce in electricity. 31 00:02:30,588 --> 00:02:36,032 And we talk about current here as a flow of postively charged particles. 32 00:02:36,032 --> 00:02:41,316 But the electrons are actually falling the other way, but we don't really care, 33 00:02:41,316 --> 00:02:45,267 we talk what's the actual value of the current that we have. 34 00:02:45,267 --> 00:02:50,576 The unit of current was named for the physicist Ampere usually denoted by a 35 00:02:50,576 --> 00:02:53,738 capital A. 1 volt is not a very big voltage. 36 00:02:53,738 --> 00:02:59,762 I'm going to show you some batteries in a second and they're typically 1 1/2 volts, 37 00:02:59,762 --> 00:03:02,757 1 ampere of current though is a lot of current. 38 00:03:02,757 --> 00:03:09,447 typically most circuits you can range from the microamp range to the milliamp 39 00:03:09,447 --> 00:03:15,888 range, 1 ampere occurs in things that are coming out of the wall, for example, and 40 00:03:15,888 --> 00:03:20,620 supply a lot of current. That in, out of a power cycle. 41 00:03:20,620 --> 00:03:24,589 Now, how the charged particles actually flow 42 00:03:24,589 --> 00:03:30,820 to in response to an applied voltage depends on the conducting medium. 43 00:03:30,820 --> 00:03:36,379 We can go through several circuit elements there are and, the laws of 44 00:03:36,379 --> 00:03:41,243 Physics determine how the voltage and current are related to each other so it's 45 00:03:41,243 --> 00:03:45,433 not always true that if you have a positive voltage, like I've indicated 46 00:03:45,433 --> 00:03:50,199 over here, that the electrons all would, rather the positively charged particles, 47 00:03:50,199 --> 00:03:52,472 always flow that way. That's not true, 48 00:03:52,472 --> 00:03:56,382 it depends on what's in between and we'll see that in just a second. 49 00:03:56,382 --> 00:04:03,730 So let's define a convention here. So, here we have a generic circuit 50 00:04:03,730 --> 00:04:08,228 element, I don't know in detail what it is but 51 00:04:08,228 --> 00:04:15,822 there's a very important convention here. And that is if you define voltage to be 52 00:04:15,822 --> 00:04:20,837 plus to minus that way, you want to defined the positive current 53 00:04:20,837 --> 00:04:23,788 as going in the positive side of the voltage. 54 00:04:23,788 --> 00:04:28,956 This is a convention that is extremely important to follow while we are getting 55 00:04:28,956 --> 00:04:32,078 used to circuits and, and have to think about them. 56 00:04:32,078 --> 00:04:37,272 This does not mean that the voltage V is going to lined up being positive number 57 00:04:37,272 --> 00:04:42,096 The way you assign voltage is up to you, you could turn out that once you put it 58 00:04:42,096 --> 00:04:46,642 in the circuit and you figure out how it works, the voltage is negative. 59 00:04:46,642 --> 00:04:50,851 And it could, of course, turn out that the current is negative, too. 60 00:04:50,851 --> 00:04:55,962 But in order to find, what we call, the v-i relations, the relationship between 61 00:04:55,962 --> 00:05:01,833 voltage and current that a given circuit element imposes, we must but, go by this 62 00:05:01,833 --> 00:05:06,684 convention. So, let's talk about some rather simple 63 00:05:06,684 --> 00:05:11,774 circuit elements first. At first, there's just a wire. 64 00:05:11,774 --> 00:05:17,442 So, we notice the word here, ideal. This is an ideal wire. 65 00:05:17,442 --> 00:05:23,769 So, an ideal wire lets any current flow that the circuit wants to flow with no 66 00:05:23,769 --> 00:05:29,047 voltage drop, the voltage is zero. The current essentially pushed through 67 00:05:29,047 --> 00:05:32,404 here with no electric potential being required. 68 00:05:32,404 --> 00:05:37,012 This is an ideal wire, this is, in fact, what a super conductor is. 69 00:05:37,012 --> 00:05:42,572 It allows current flow with no voltage to be applied, no voltage drop. 70 00:05:42,572 --> 00:05:49,377 the real wire has a small resistance and does not behave like this at all. 71 00:05:49,377 --> 00:05:55,787 But this is what we use in circuits. This is a model of an ideal circuit 72 00:05:55,787 --> 00:06:02,318 element what's called, we called the short circuit that let's any current go 73 00:06:02,318 --> 00:06:09,900 at all, but the voltage drop is zero. And guess that there's also an open 74 00:06:09,900 --> 00:06:19,119 circuit which is what I call a dead wire. Which, in this case, there's no current 75 00:06:19,119 --> 00:06:25,400 flowing because it's open, it's free space that will be in between, but there 76 00:06:25,400 --> 00:06:29,841 is a voltage drop. And the voltage drop can be anything that 77 00:06:29,841 --> 00:06:34,173 the circuit, in which this open circuit is found, can occur. 78 00:06:34,173 --> 00:06:39,999 and so the important point here is that in an open circuit, there is no current 79 00:06:39,999 --> 00:06:46,186 flow through the open area, i = 0. Okay. Well, let's talk about something 80 00:06:46,186 --> 00:06:52,881 that actually does something perhaps the simpliest circuit element is the 81 00:06:52,881 --> 00:06:56,732 resistor. And here, voltage and current are 82 00:06:56,732 --> 00:07:04,005 proportionate to one another and the constant of proportionality is the 83 00:07:04,005 --> 00:07:09,423 resistance R. So, 1 ohm is a volt divided by an amp, 1 84 00:07:09,423 --> 00:07:14,274 ampere. 1 volt divided by 1 ampere is 1 ohm and 85 00:07:14,274 --> 00:07:22,623 the symbol for an ohm is a capital Omega. so, very simple circuit element 86 00:07:22,623 --> 00:07:28,230 as we'll see when I show you some low ones in just a second. 87 00:07:28,230 --> 00:07:32,865 The capacitor, and, it was a bit more interesting. 88 00:07:32,865 --> 00:07:40,857 the symbol for a capacitor is this set of, lines, going into what looks like two 89 00:07:40,857 --> 00:07:46,582 perpendicular lines. The v-i relationship is that the current 90 00:07:46,582 --> 00:07:50,682 is proportional to the derivative of voltage. 91 00:07:50,682 --> 00:07:55,772 And the constant of proportionality is the capacitance, 92 00:07:55,772 --> 00:08:01,480 which is measured in Farads. Farads is named from Michael Faraday, a 93 00:08:01,480 --> 00:08:06,217 very important 19th century experimental physicist. 94 00:08:06,217 --> 00:08:12,871 Now, how do you build a capacitor? Well, it turns out the symbol for the capacitor 95 00:08:12,871 --> 00:08:17,909 gives it away. If you had two parallel plates and you 96 00:08:17,909 --> 00:08:24,713 put leads to them and apply the voltage to it, put it in a circuit, 97 00:08:24,713 --> 00:08:30,843 what's happened is that charge wants to accumulate on this plate. 98 00:08:30,843 --> 00:08:36,532 and it may, the current actually doesn't flow through. 99 00:08:36,532 --> 00:08:43,054 It doesn't jump across those plates, but current can slosh back and forth as if it 100 00:08:43,054 --> 00:08:49,435 were flowing through the circuit element. And it turns out the capacitance C is 101 00:08:49,435 --> 00:08:56,222 equal to the dielectric constant of the mediumness in between times the area of 102 00:08:56,222 --> 00:09:00,976 the plates divided the distance between them. 103 00:09:00,976 --> 00:09:10,935 So in order to get the capacitance up, you have to have a big area and/or a very 104 00:09:10,935 --> 00:09:19,855 small distance between the two plates. Now, I give you an idea about scale here, 105 00:09:19,855 --> 00:09:24,817 a 1 Farad capacitor is huge, it's gigantic. 106 00:09:24,817 --> 00:09:28,911 And that is the way the units all work out. 107 00:09:28,911 --> 00:09:36,087 typically capacitors are in the millifarad, that's a pretty big capacitor 108 00:09:36,087 --> 00:09:42,421 even microfarad, even nanofarads, and even picofarad capacitors are founding 109 00:09:42,421 --> 00:09:47,448 lots and lots of circuits. But that's the way they're constructed 110 00:09:47,448 --> 00:09:52,286 out of parallel plates. This goes back to what I said about the 111 00:09:52,286 --> 00:09:56,262 nature of the medium for the circuit element. 112 00:09:56,262 --> 00:10:02,484 It defines that the i relationship resistor is probably the simplest medium 113 00:10:02,484 --> 00:10:09,445 and capacitor is an interesting medium, too, that has a bit more complicated v-i 114 00:10:09,445 --> 00:10:13,737 relation. And then finally, there's the inductor. 115 00:10:13,737 --> 00:10:20,127 inductors are the symbol here for an inductor is supposed to resemble a coiled 116 00:10:20,127 --> 00:10:25,457 wire, has an inductance, L, which is measured in Henrys, named for Joseph 117 00:10:25,457 --> 00:10:29,312 Henry, an American 19th century physicist. 118 00:10:29,312 --> 00:10:35,052 And it has a v-i relationship, the voltage is proportional to the derivative 119 00:10:35,052 --> 00:10:37,929 current. In some sense, it's the opposite of a 120 00:10:37,929 --> 00:10:40,902 capacitor. And if we use the laws of Physics to 121 00:10:40,902 --> 00:10:45,679 figure out how voltage and current are related when there's a coil of wire, 122 00:10:45,679 --> 00:10:49,479 we'll discover that at the new approximation, the voltage is 123 00:10:49,479 --> 00:10:52,519 proportional to the derivative of the current. 124 00:10:52,519 --> 00:10:56,866 So inductors are found, for example, in, in 125 00:10:56,866 --> 00:11:02,688 automobiles, when you talk about the coil in an automobile, it turns out it's a big 126 00:11:02,688 --> 00:11:06,306 inductor. Okay. So, let me show you some resistors. 127 00:11:06,306 --> 00:11:11,862 So, here's a photograph I took of the set of resistors I happen to have. And I want 128 00:11:11,862 --> 00:11:15,972 you to notice, first of all, they're all the same size, 129 00:11:15,972 --> 00:11:21,853 no matter how big the resistance is. So, this is the actual resistance of each 130 00:11:21,853 --> 00:11:28,306 of these circuit elements resistors rather going all the way from 10 ohms to 131 00:11:28,306 --> 00:11:32,024 1 megaohm. I want to hold up a resistor to give you 132 00:11:32,024 --> 00:11:36,812 an idea of the size. This happens to be the 1 megaohm resistor 133 00:11:36,812 --> 00:11:43,731 that I showed you in the photograph here and you can see, it's pretty small. 134 00:11:43,731 --> 00:11:49,218 The size of the resistor determines how much power you can dissipate. 135 00:11:49,218 --> 00:11:54,755 These turned out to be 1/4 watt resistors and we'll talk about the power 136 00:11:54,755 --> 00:12:00,377 considerations in a second. Well, how did I know that these are the 137 00:12:00,377 --> 00:12:06,982 values of the resistors? And I don't know if you could see it very well but there 138 00:12:06,982 --> 00:12:14,617 are little bands of color going around each of the elements and it turns out 139 00:12:14,617 --> 00:12:19,952 that brown black orange is a 10,000 ohm resistor. 140 00:12:19,952 --> 00:12:26,141 And this round black red here turns out to be a 1 kilo ohm resistor. 141 00:12:26,141 --> 00:12:30,242 So, I'm reading those colors from the top. 142 00:12:30,242 --> 00:12:37,393 This is called the color code. And you can go online and Google color 143 00:12:37,393 --> 00:12:40,766 code. And you'll find lots of calculators, what 144 00:12:40,766 --> 00:12:45,583 are called calculators for color codes. You type in the colors, and they'll tell 145 00:12:45,583 --> 00:12:49,887 you what the resistance is, or you can type in the resistance and they'll tell 146 00:12:49,887 --> 00:12:54,069 you what the colors are. And you should remember them as you get deeper into 147 00:12:54,069 --> 00:12:57,993 Electrical Engineering. but the important thing here is size does 148 00:12:57,993 --> 00:13:03,202 not determine the resistance. The turn is the size of a resistor is the 149 00:13:03,202 --> 00:13:09,077 most power, it dissipates. And I'm showing that in the next slide, 150 00:13:09,077 --> 00:13:16,502 where I have a much bigger resistor. So, here's that resistor and you can see 151 00:13:16,502 --> 00:13:21,162 it's quite, it's much bigger than the other resistors 152 00:13:21,162 --> 00:13:24,907 I have. And, if you look at it very carefully, 153 00:13:24,907 --> 00:13:31,227 you can see it says, it's 75 ohms and I don't know if you can see it very well, 154 00:13:31,227 --> 00:13:37,082 but down below, what I just the wrote over, it says, it's 25 watts. 155 00:13:37,082 --> 00:13:41,647 So, this will, will dissipate lots of the power. 156 00:13:41,647 --> 00:13:48,757 It turns out it's hollow inside and that's there to allow more power to 157 00:13:48,757 --> 00:13:54,547 dissipate from this. So, this is able to put out lots of 158 00:13:54,547 --> 00:13:58,962 power. I'm sure you've seen light bulbs. 159 00:13:58,962 --> 00:14:05,766 in the US, there's 60- watt light bulbs, and they can get very warm, very quickly. 160 00:14:05,766 --> 00:14:09,383 Imagine at 25 watts can also get pretty warm. 161 00:14:09,383 --> 00:14:13,571 These 1/4 wire resistors don't get very warm at all. 162 00:14:13,571 --> 00:14:18,248 So, let me show you a capacitor. And you can see on the left there, 163 00:14:18,248 --> 00:14:24,357 a 470 microfarad capacitor and it's pretty big. 164 00:14:24,357 --> 00:14:28,812 Here it is. And it's a pretty good size, bigger than 165 00:14:28,812 --> 00:14:36,657 my finger in diameter, and that's like I said, a pretty hefty sized resistor. 166 00:14:36,657 --> 00:14:43,860 On the right, is a 1 nF resistor, and which, I mean, sorry, 1 nF capacitor 167 00:14:43,860 --> 00:14:50,069 [UNKNOWN] a 1 nF capacitor. And it's small by comparison and you'll 168 00:14:50,069 --> 00:14:57,012 find that science capacitor in lots of electronic circuits. 169 00:14:57,012 --> 00:15:02,354 Finally, let me show you an inductor, and here's the inductor. 170 00:15:02,354 --> 00:15:07,888 It's in that photograph. It's about finger sized. And if you look 171 00:15:07,888 --> 00:15:14,749 at it carefully, it is a coil of wire coiled around a circular object and I 172 00:15:14,749 --> 00:15:19,585 want to point out something. if you look very carefully at this 173 00:15:19,585 --> 00:15:23,700 figure, you can see that the wires coming out look to be silverish. 174 00:15:23,700 --> 00:15:26,849 They're not really silver, but they look silverish. 175 00:15:26,849 --> 00:15:30,141 Whereas, they look to be brownish around the coil. 176 00:15:30,141 --> 00:15:34,138 And it turns out the brown does not indicate that they're copper. 177 00:15:34,138 --> 00:15:37,602 That brownish substance turns out to be an insulator. 178 00:15:37,602 --> 00:15:43,703 Because if this wire was not insulated right over here, for example, the wires 179 00:15:43,703 --> 00:15:48,955 are touching each other and it would short out the entire inductor. 180 00:15:48,955 --> 00:15:55,031 Because they're insulated, this coil of wire now looks like an inductor and 181 00:15:55,031 --> 00:16:00,283 you'll find this, it applies very consistently throughout Electrical 182 00:16:00,283 --> 00:16:05,674 Engineering, that when you send to see if that kind of color it's indicating that 183 00:16:05,674 --> 00:16:10,936 it's a insultated wire, you can scrape if off if you want to get 184 00:16:10,936 --> 00:16:14,974 rid of the insulation. Also, as you know, there's a plastic kind 185 00:16:14,974 --> 00:16:20,685 of installation and lots of lines, too. But in this special case, it would 186 00:16:20,685 --> 00:16:26,095 indicate that this is a very small kind or, kind of insulator, too. 187 00:16:26,095 --> 00:16:32,383 Okay, let's go back and look at the circuit elements again, because there are 188 00:16:32,383 --> 00:16:40,690 times when you want to write the v-i relations the other way if you will. So, 189 00:16:40,690 --> 00:16:47,883 instead of v = Ri, you might want to write i equals 1 / R * v. 190 00:16:47,883 --> 00:16:54,472 Well, we call 1 / R is called the conductance. 191 00:16:54,472 --> 00:17:02,719 It's given the symbol G and G is measured in Siemens, a name for the German 192 00:17:02,719 --> 00:17:12,036 inventor of designer of telegraph systems in the early part of the 19th century. 193 00:17:12,036 --> 00:17:17,452 So, the symbol G is for Siemens. There are going to be lots of times when 194 00:17:17,452 --> 00:17:21,897 it's more convenient to think about a resistor in terms of its conductance 195 00:17:21,897 --> 00:17:25,757 reciprocal ohms, Siemens, that it is in terms of its resistance. 196 00:17:25,757 --> 00:17:30,147 And we'll find that out very soon. Now, of course, for the capacitor and the 197 00:17:30,147 --> 00:17:36,418 inductor, those derivative relationships turn into integral relationships and as I 198 00:17:36,418 --> 00:17:42,865 said, all integrals in this correspond, definite integrals and they all start at 199 00:17:42,865 --> 00:17:46,685 minus infinity. So, in some sense, a voltage and a 200 00:17:46,685 --> 00:17:52,868 capacitor has an infinite memory of all the previous ties of the current. All 201 00:17:52,868 --> 00:17:57,754 previous ties of the current, now matter how their rose, going back to 202 00:17:57,754 --> 00:18:01,954 the beginning of the big bang are summarized by the voltage. 203 00:18:01,954 --> 00:18:07,140 Of course, there are a lot of different current patterns that are results in the 204 00:18:07,140 --> 00:18:10,173 same voltage. Same thing for the inductor. 205 00:18:10,173 --> 00:18:16,734 It's the current that contains a memory of everything all the voltage values that 206 00:18:16,734 --> 00:18:19,612 the voltage of the inductors had across it. 207 00:18:19,612 --> 00:18:25,012 A kind of interesting that they have this kind of infinite memory, but that's what 208 00:18:25,012 --> 00:18:28,312 you get when you have a derivative relationship. 209 00:18:28,312 --> 00:18:30,812 Turn it around, it comes in here. Okay. 210 00:18:30,812 --> 00:18:36,266 Let's talk about some different elements, namely, sources. And these provide a 211 00:18:36,266 --> 00:18:40,402 voltage or a current to a circuit that we build. 212 00:18:40,402 --> 00:18:46,916 So, a voltage source is indicated by a circle with a, a + to - indicating the 213 00:18:46,916 --> 00:18:52,018 positive direction for the applied voltage, v sub s, 214 00:18:52,018 --> 00:18:56,386 s for source. So, the v-i relationship again, I am 215 00:18:56,386 --> 00:19:01,456 defining my own voltage v and my own current i, going to the top in a 216 00:19:01,456 --> 00:19:05,144 consistent way, is that the voltage is going to equal to 217 00:19:05,144 --> 00:19:10,707 whatever the source is for all i. So, what this means is that the voltage 218 00:19:10,707 --> 00:19:14,357 source has no constraints at all in the current. 219 00:19:14,357 --> 00:19:19,892 It can supply any current that the circuit to which this voltage source is 220 00:19:19,892 --> 00:19:26,812 attached will want what it does is it provides a, a voltage for all of the 221 00:19:26,812 --> 00:19:28,776 time, whatever v sub s is. 222 00:19:28,776 --> 00:19:34,384 Similar thing for a current source, is that this will provide a current no 223 00:19:34,384 --> 00:19:38,682 matter what the voltage is. The voltage could be 0 -100. 224 00:19:38,682 --> 00:19:41,209 10^-6. It really doesn't matter. 225 00:19:41,209 --> 00:19:46,901 It's going to provide a given current. Now, notice the little minus sign here 226 00:19:46,901 --> 00:19:51,667 and that is because, on this, the way I've drawn it, i sub s, is a 227 00:19:51,667 --> 00:19:56,892 positive current from the way and we always want i defining the v-i relation 228 00:19:56,892 --> 00:20:01,892 to get on the positive side of voltage. So, these two currents are going the 229 00:20:01,892 --> 00:20:05,717 opposite way and that's the reason for that minus sign. 230 00:20:05,717 --> 00:20:10,257 It's just a minor little thing. I just want to make sure you're 231 00:20:10,257 --> 00:20:15,242 consistent in the way you define things. Let me point out it is very, very 232 00:20:15,242 --> 00:20:18,254 important that you, you define voltage that way, 233 00:20:18,254 --> 00:20:23,720 you define current only in the positive sign of a volt, very, very important. 234 00:20:23,720 --> 00:20:29,877 Now, let's look at some batteries. So, batteries are a special case of a 235 00:20:29,877 --> 00:20:35,047 voltage source that produce constant voltages. 236 00:20:35,047 --> 00:20:40,202 And I've got 4 batteries in this photograph. 237 00:20:40,202 --> 00:20:45,432 This is a D-cell, which is, as you know, pretty big, 238 00:20:45,432 --> 00:20:50,312 is gives you a size of scale. If you read the label very carefully, it 239 00:20:50,312 --> 00:20:54,143 says 1 and a 1/2 volts. The little button at the top is the 240 00:20:54,143 --> 00:20:57,557 positive side. It doesn't, in most cases, they don't 241 00:20:57,557 --> 00:21:01,897 label the negative side. Once you know what's positive, the other 242 00:21:01,897 --> 00:21:05,459 end is negative. This is a AAA battery and if you look 243 00:21:05,459 --> 00:21:09,782 very carefully right there, it says, it's also 1 and a 1/2 volts. 244 00:21:09,782 --> 00:21:15,237 So, again, the size of the battery does not determine the size of the voltage it 245 00:21:15,237 --> 00:21:19,204 produces. what it does tell you is how long the, 246 00:21:19,204 --> 00:21:24,738 each battery will provide that voltage. Basically, the bigger the battery, the 247 00:21:24,738 --> 00:21:27,477 more [UNKNOWN] as I like to think about it, 248 00:21:27,477 --> 00:21:30,832 the more [UNKNOWN] it possesses, it can last longer. 249 00:21:30,832 --> 00:21:36,752 Chemical reactions can be sustained. So, the AAA battery, in general in a 250 00:21:36,752 --> 00:21:42,803 circuit won't last as a, as long as a D size battery attached to the same 251 00:21:42,803 --> 00:21:46,811 circuit. I wanted to point out, I discovered this 252 00:21:46,811 --> 00:21:54,101 the other day this is a battery that goes into my remote control for my doorlock on 253 00:21:54,101 --> 00:21:57,557 my car. And if you look at it very carefully 254 00:21:57,557 --> 00:22:02,228 right there, it says, 12 volts. So, this actually provides a bigger 255 00:22:02,228 --> 00:22:07,113 voltage than a triple A and than a D-cell, but it doesn't provide much 256 00:22:07,113 --> 00:22:10,850 current. by the way, the 27A that you may see at 257 00:22:10,850 --> 00:22:16,080 the top of this battery, is a model but it does not mean it provides 27 amps, I 258 00:22:16,080 --> 00:22:21,650 guarantee you it doesn't. And finally, this rectangular battery we 259 00:22:21,650 --> 00:22:26,400 see is clearly labeled 9v. And on the side, you can look to see 260 00:22:26,400 --> 00:22:32,368 which end is positive and which end is negative, that's labeled on the side of 261 00:22:32,368 --> 00:22:36,121 the battery. Okay. You can buy these clearly at any 262 00:22:36,121 --> 00:22:38,641 store. They're readily available. 263 00:22:38,641 --> 00:22:42,521 So, don't forget that when you buy a battery like this, 264 00:22:42,521 --> 00:22:47,008 it's open-circuited, there's nothing attached to, between the 265 00:22:47,008 --> 00:22:50,102 top and bottom. There's no, nothing there. 266 00:22:50,102 --> 00:22:55,460 So, for here, the way it's been pictured, the current is 0 because there's nothing 267 00:22:55,460 --> 00:22:59,028 attached to it. These batteries are quite happy to 268 00:22:59,028 --> 00:23:05,944 produce 1 and a 1/2 volts for these two, at least no matter what because they are 269 00:23:05,944 --> 00:23:10,269 just sitting there. Now, how about a current source? Well, a 270 00:23:10,269 --> 00:23:17,528 current source will provide a current no matter what voltage is across it. 271 00:23:17,528 --> 00:23:26,199 Providing a current means there's flow of charged particles going out of this 272 00:23:26,199 --> 00:23:31,379 device. It, if you, if it's open-circuited, where 273 00:23:31,379 --> 00:23:38,389 are these charged particles, electrons going? Where do they go? if it's really 274 00:23:38,389 --> 00:23:44,146 open, the current source has a real problem, it has no place for the current 275 00:23:44,146 --> 00:23:47,886 to go. Remember, an open circuit does not allow 276 00:23:47,886 --> 00:23:53,817 any current so it's inconsistent. So, it is very hard to go to a store and 277 00:23:53,817 --> 00:23:58,316 buy yourself a current source that's sitting here like this. 278 00:23:58,316 --> 00:24:03,921 It would be perfectly happy if the current source were short-circuited. 279 00:24:03,921 --> 00:24:09,802 You could buy one of those but heaven forbid, if you tried to break that wire 280 00:24:09,802 --> 00:24:14,772 off to attach it to something because then it would not be very happy. 281 00:24:14,772 --> 00:24:22,051 So, current sources are hard to buy in one sense and you go back to the voltage 282 00:24:22,051 --> 00:24:26,164 source. So, a voltage source is very happy to be 283 00:24:26,164 --> 00:24:31,648 open-circuited but it does not like to be short-circuited. 284 00:24:31,648 --> 00:24:38,867 So, this means the current flows, no matter what will a short circuit is a 285 00:24:38,867 --> 00:24:45,072 0 valued resistor, so this means that the voltage, in order 286 00:24:45,072 --> 00:24:53,372 for v = Ri, if we have a positive voltage, let's say, provided by this 287 00:24:53,372 --> 00:25:00,295 source and the resistance is whatever it is, it's 0 for short circuit. 288 00:25:00,295 --> 00:25:06,725 Well, to get a pop and number here, this current would have to be infinite to make 289 00:25:06,725 --> 00:25:11,650 everything work out. And so, voltage sources do not want to be 290 00:25:11,650 --> 00:25:16,147 short-circuited. Current sources do not want to be 291 00:25:16,147 --> 00:25:20,497 open-circuited. Voltage sources do not want to be 292 00:25:20,497 --> 00:25:23,497 short-circuited, fundamentals of Electrical Engineering. 293 00:25:24,847 --> 00:25:28,697 Okay. So, let's talk about power and energy. 294 00:25:28,697 --> 00:25:36,127 Now, the conservation of energy principle is that the sum of energies, consumed or 295 00:25:36,127 --> 00:25:39,852 produced in a closed system, is a constant. 296 00:25:39,852 --> 00:25:47,027 So you can't produce energy from nothing. A closed system means there's nothing 297 00:25:47,027 --> 00:25:52,777 going in or out of this system and whatever energy is inside that close 298 00:25:52,777 --> 00:25:52,777 system is going to be constant for all times. 299 00:25:54,252 --> 00:26:02,183 So what is power? Power is the rate of change of energy 300 00:26:02,183 --> 00:26:13,052 with time. So that's just the definition. So, p is usually measured in watts. 301 00:26:13,052 --> 00:26:20,644 And to be consistent with this definition, the energy would be in 302 00:26:20,644 --> 00:26:24,713 joules. And time would be in seconds. 303 00:26:24,713 --> 00:26:29,725 So, a watt is a joule second, joules per second. 304 00:26:29,725 --> 00:26:37,547 And, but the important thing for here is that the power and the conservation of 305 00:26:37,547 --> 00:26:44,387 energy principle that the energy is a constant means that That in a closed 306 00:26:44,387 --> 00:26:50,702 system, the power, total power in that system is zero at all times. 307 00:26:50,702 --> 00:26:57,314 Inside that closed system, there could be parts of it that are producing energy, 308 00:26:57,314 --> 00:27:00,933 producing power, but other parts have to consume it. 309 00:27:00,933 --> 00:27:06,070 They have to consume that power, so we should look in circuits and what I'm 310 00:27:06,070 --> 00:27:10,701 going to show a little bit later is that this law is obeyed by circuits. 311 00:27:10,701 --> 00:27:15,412 whatever is producing the power is also consuming it somewhere else. 312 00:27:15,412 --> 00:27:23,433 That's just the way things have to be. Well, what's the definition of power for 313 00:27:23,433 --> 00:27:28,613 a circuit? So, definition. The instantaneous power, 314 00:27:28,613 --> 00:27:36,521 the power at time t that is dissipated by a circuit element is the voltage times 315 00:27:36,521 --> 00:27:43,224 the current at those same times. Now notice the word, dissipated. 316 00:27:43,224 --> 00:27:49,249 So, positive power, if p is greater than 0, that means you're 317 00:27:49,249 --> 00:27:53,552 dissipating power. If p of t is less than 0, 318 00:27:53,552 --> 00:28:00,752 that means it's producing power and that's the convention, that's the way to 319 00:28:00,752 --> 00:28:05,987 think about it. Go back to the derivative convention for 320 00:28:05,987 --> 00:28:13,422 relationship between power and energy. So, if power is positive that means the 321 00:28:13,422 --> 00:28:20,659 energy being consumed by the whatever elements going up, so it's consuming, 322 00:28:20,659 --> 00:28:26,729 but it is less than it's producing so it's all very consistent. 323 00:28:26,729 --> 00:28:32,560 What's interesting is that watts is equal to volts times amperes. 324 00:28:32,560 --> 00:28:39,222 So, we measure the voltage in volts, the current in amperes, multiply them 325 00:28:39,222 --> 00:28:45,910 together and you get the power being dissipated or produced by that circuit 326 00:28:45,910 --> 00:28:52,162 element at that time. So let's go through the various elements 327 00:28:52,162 --> 00:28:56,782 and see what the power equations are for them. 328 00:28:56,782 --> 00:29:04,387 So, for a resistor where v = Ri, you can put, substitute this into the power 329 00:29:04,387 --> 00:29:12,676 formula up here anyway you want and what you get is that the power is either Ri^2, 330 00:29:12,676 --> 00:29:19,255 Rv^2 / R, whichever way you want to think about it in terms of voltage and current. 331 00:29:19,255 --> 00:29:25,370 So, one thing to point out, squaring always gives a nonzero, non, a positive 332 00:29:25,370 --> 00:29:32,172 quantity, it cannot be negative and that means the resistors always dissipate 333 00:29:32,172 --> 00:29:38,116 power. And that's why the wattage of the resistor is very important to consider 334 00:29:38,116 --> 00:29:44,042 because it's going to dissipate power and you'd better have a physical design for 335 00:29:44,042 --> 00:29:49,904 your resistor so that it can let the power dissipate freely up to its stated 336 00:29:49,904 --> 00:29:53,031 rating. But it always dissipates. So, resistors 337 00:29:53,031 --> 00:30:00,466 make dissipate power so there has to be some other element in the circuit that 338 00:30:00,466 --> 00:30:05,244 produces the power that the resistors dissipate. 339 00:30:05,244 --> 00:30:12,527 If we look at the capacitor, and the inductor things are a bit more 340 00:30:12,527 --> 00:30:19,687 interesting. So, I, I plugged let's say, the derivative relationship in here and 341 00:30:19,687 --> 00:30:25,108 it will, a little manipulation to show you that the power consumed by a 342 00:30:25,108 --> 00:30:30,620 capacitor is related to the derivative of the square of the voltage. 343 00:30:30,620 --> 00:30:36,322 So now, the square of a voltage, of course, again, is a positive number. 344 00:30:36,322 --> 00:30:40,881 However, it's derivitive can be both positive and negative. 345 00:30:40,881 --> 00:30:46,884 So, there are times when a capacitor can actually produce energy, produce power, 346 00:30:46,884 --> 00:30:52,735 and there are times when it consumes it. It depends on the nature of V and it's 347 00:30:52,735 --> 00:30:57,985 the same for the inductor. And, in fact, the way that we think about 348 00:30:57,985 --> 00:31:04,907 these, these are energy storage devices, the inductor and the capacitor. 349 00:31:04,907 --> 00:31:12,646 And capacitor energy is stored in the voltage and an inductor is stored, stored 350 00:31:12,646 --> 00:31:16,807 in the current. and these are results, 351 00:31:16,807 --> 00:31:24,605 these equations tell you how to calculate the power that's consumed or produced by 352 00:31:24,605 --> 00:31:30,232 these various elements. Now, I want to show you how we are going 353 00:31:30,232 --> 00:31:33,382 to start thinking about these. So, 354 00:31:33,382 --> 00:31:40,142 our fundamental circuit elements are going to be the resistor, the capacitor, 355 00:31:40,142 --> 00:31:44,575 and the inductor. We'll use voltage sources a lot. 356 00:31:44,575 --> 00:31:51,602 Now, we are going to build systems out of these elements that's called a circuit. 357 00:31:51,602 --> 00:32:00,553 Now so, all of these elements will go into our system. 358 00:32:00,553 --> 00:32:08,677 the sources, they're the ones that provide the signal 359 00:32:08,677 --> 00:32:17,891 for the input to the system and we'll somehow grab the voltage or currant to be 360 00:32:17,891 --> 00:32:23,649 the output of the system. So, the sources provide the input x and 361 00:32:23,649 --> 00:32:29,823 we'll all going to, have to figure out how you build systems that have been 362 00:32:29,823 --> 00:32:36,398 resistors, conductors, and capacitors in order to accomplish some goal, some 363 00:32:36,398 --> 00:32:41,687 relationship between x and y that you want and then, some voltage or current 364 00:32:41,687 --> 00:32:44,642 will be in the output. That's what's coming next. 365 00:32:44,642 --> 00:32:49,763 We'll try to build real circuits and try to do something useful with them.