1 00:00:01,800 --> 00:00:04,140 Welcome back to our series in linear circuits. 2 00:00:04,140 --> 00:00:06,813 Again, I'm Nathan Parish. And today we're going to be talking about 3 00:00:06,813 --> 00:00:10,777 an Introduction to Circuit Diagrams. We'll start looking at the actual things 4 00:00:10,777 --> 00:00:13,801 that are drawn out, and really get your hands in there trying to solve some of 5 00:00:13,801 --> 00:00:17,085 these things. The things we're going to be aiming to do 6 00:00:17,085 --> 00:00:21,070 today is to identify the collection of basic circuit elements. 7 00:00:21,070 --> 00:00:25,023 To be able to identify nodes, identify short and open circuits, and then finally 8 00:00:25,023 --> 00:00:30,813 to identify equivalent circuit diagrams. So from last class, we showed how 9 00:00:30,813 --> 00:00:34,047 currents and voltage interact to let us know the power that's being consumed by 10 00:00:34,047 --> 00:00:37,213 the system. And we showed the basic physical 11 00:00:37,213 --> 00:00:41,630 constraints and equations that allow us to solve for unknown values. 12 00:00:41,630 --> 00:00:44,798 In that case, it was using a known power and a known voltage for example, to be 13 00:00:44,798 --> 00:00:50,010 able to find a current. So now we're going to be taking all of 14 00:00:50,010 --> 00:00:52,862 the things that we've learned to this point and starting to look at how they 15 00:00:52,862 --> 00:00:56,570 come together into an actual circuit diagram. 16 00:00:56,570 --> 00:00:59,545 Which is probably the thing that you most think of when you think about circuits. 17 00:00:59,545 --> 00:01:02,617 In this lesson, our objectives are to identify a set of circuit elements, the 18 00:01:02,617 --> 00:01:05,833 ones that we're going to be presenting, which will be all of the circuit elements 19 00:01:05,833 --> 00:01:11,330 that we'll be looking at in the class. But enough to get us started. 20 00:01:11,330 --> 00:01:14,747 We'll identify nodes in a circuit diagram and recognize which circuits are self 21 00:01:14,747 --> 00:01:19,420 contradictory or circuits that just don't really make sense. 22 00:01:19,420 --> 00:01:23,019 We'll identify open and closed circuits, identify when two circuits are 23 00:01:23,019 --> 00:01:27,640 equivalent, and modify a circuit to give us an equivalent circuit. 24 00:01:29,000 --> 00:01:31,100 So first of all, we just present this circuit diagram. 25 00:01:31,100 --> 00:01:33,895 Now, you don't know what any of these things mean if you haven't been presented 26 00:01:33,895 --> 00:01:37,590 a little bit of information on circuits before now. 27 00:01:37,590 --> 00:01:40,406 But these are all circuits that we are going to be looking at today, and then we 28 00:01:40,406 --> 00:01:43,090 will revisit this diagram after we've been able to see all the individual 29 00:01:43,090 --> 00:01:46,610 components. To see how they come and work together. 30 00:01:48,280 --> 00:01:51,320 So first of all, let's actually define what we mean by circuit analysis. 31 00:01:51,320 --> 00:01:54,309 We kind of use the term a little bit loosely here, but let's kind of pin down 32 00:01:54,309 --> 00:01:58,191 what we mean. And devices that are given some known 33 00:01:58,191 --> 00:02:02,780 parameters and we put them all together in kind of a graphical model. 34 00:02:02,780 --> 00:02:07,830 And we wish to identify the behavior with this device using the known information. 35 00:02:07,830 --> 00:02:11,262 So what we're going to be then doing are making systems of equations to describe 36 00:02:11,262 --> 00:02:15,500 the behavior, and then solving these different equations. 37 00:02:15,500 --> 00:02:18,228 To let us know the unknown values, the things that we're eager to discover, 38 00:02:18,228 --> 00:02:23,307 about how the circuit's going to behave. So the first element we're going to be 39 00:02:23,307 --> 00:02:26,281 looking at, is wires. In the circuit diagram, wires are 40 00:02:26,281 --> 00:02:30,280 presented as lines. And they just connect the devices. 41 00:02:30,280 --> 00:02:34,072 And they hold them all together. Wires are believed to have zero internal 42 00:02:34,072 --> 00:02:36,752 resistance. Which means that current can just flow 43 00:02:36,752 --> 00:02:39,305 through it. And it doesn't really have any impact in 44 00:02:39,305 --> 00:02:41,970 and of itself. It's just a way to show two different 45 00:02:41,970 --> 00:02:46,805 items are connected together. You also have these two terms, nodes and 46 00:02:46,805 --> 00:02:50,270 junctions. By nodes we mean any set of wires that's 47 00:02:50,270 --> 00:02:54,358 all connected together. And a junction is where we see two wires 48 00:02:54,358 --> 00:02:58,895 that actually meet up. So here, this would be a junction, a 49 00:02:58,895 --> 00:03:01,480 little dot. And we'll use these filled in dots to 50 00:03:01,480 --> 00:03:04,375 indicate where these two wires are actually connected. 51 00:03:04,375 --> 00:03:08,509 But all of this is a node, and so sometimes they can be a little bit 52 00:03:08,509 --> 00:03:13,220 difficult to distinguish what the nodes are. 53 00:03:13,220 --> 00:03:16,010 So one thing that can be helpful is color them. 54 00:03:16,010 --> 00:03:21,210 So here we have the red node, everything that is red is part of the same node. 55 00:03:21,210 --> 00:03:23,015 Everything that's green is part of the same node. 56 00:03:23,015 --> 00:03:26,330 Anf everything here that is blue is all part of one node. 57 00:03:26,330 --> 00:03:29,000 So even though we have a couple different junctions here, those aren't the nodes. 58 00:03:30,080 --> 00:03:33,473 The node is everything that's connected together. 59 00:03:33,473 --> 00:03:36,753 And we believe that this node, there is zero voltage. 60 00:03:36,753 --> 00:03:41,670 And if you remember, voltage is created by differences in charge density. 61 00:03:41,670 --> 00:03:44,476 Well, because charge is able to freely flow on a wire, it can redistribute 62 00:03:44,476 --> 00:03:47,892 itself however it see's fit. And so what's going to happen is all the 63 00:03:47,892 --> 00:03:51,890 Charge is going to just distribute itself as broadly as possible. 64 00:03:51,890 --> 00:03:54,669 And so we get no voltage across any different wire. 65 00:03:55,720 --> 00:03:58,681 And it's also possible to have an arbitrarily large current that makes this 66 00:03:58,681 --> 00:04:01,658 happen. We place no constraints on these 67 00:04:01,658 --> 00:04:04,395 particular wires. Now, obviously that's not true for 68 00:04:04,395 --> 00:04:06,486 physical wires. If I tried to stick a very enormous 69 00:04:06,486 --> 00:04:09,690 current through a physical wire, bad things happen. 70 00:04:09,690 --> 00:04:12,445 But as far as our diagrams are concerned, it's perfectly fine. 71 00:04:12,445 --> 00:04:17,210 The next devices that we're going to look at are independent sources. 72 00:04:17,210 --> 00:04:20,474 That these sources are sources where we specify either a current or a voltage 73 00:04:20,474 --> 00:04:25,790 that is believed to constant, no matter what else is going on in the system. 74 00:04:25,790 --> 00:04:29,024 So the first one, where we have the plus and the minus, is an independent voltage 75 00:04:29,024 --> 00:04:31,866 source, where we say that the voltage from the minus to the plus is some 76 00:04:31,866 --> 00:04:36,010 constant voltage. And it's completely independent of 77 00:04:36,010 --> 00:04:40,250 anything else going on in the system, however it might be a function of time. 78 00:04:40,250 --> 00:04:43,240 For example, you might have some type of device variable which is going to go up 79 00:04:43,240 --> 00:04:46,276 and down in time, but nothing else in the circuit is going to be able to determine 80 00:04:46,276 --> 00:04:51,340 what that voltage is going to be. It's kind of a known value. 81 00:04:51,340 --> 00:04:53,877 The same thing is said for current sources, but in this case we're again 82 00:04:53,877 --> 00:04:57,004 going to use an arrow. And these designations, the plus and the 83 00:04:57,004 --> 00:04:59,902 minus and the arrow, correspond to the same pluses and minuses and arrows we 84 00:04:59,902 --> 00:05:03,770 were using before when we discussed both voltages and currents. 85 00:05:05,270 --> 00:05:08,330 Sometimes we don't know for certain what these values are, but they are actually a 86 00:05:08,330 --> 00:05:12,170 function of something else that's going on in the circuit. 87 00:05:12,170 --> 00:05:16,210 So, when we have this happen, we use what are called Dependent sources. 88 00:05:16,210 --> 00:05:21,080 Instead of using circles, we now use squares that are turned on their angle. 89 00:05:21,080 --> 00:05:23,645 So, again, we have, on the left, a voltage source with the plus and the 90 00:05:23,645 --> 00:05:27,250 minus, and then, on the right, a current source, with an arrow. 91 00:05:28,430 --> 00:05:31,374 These will typically be described by using some kind of equation that will be 92 00:05:31,374 --> 00:05:35,638 listed next to the device. Referencing some other measured quantity 93 00:05:35,638 --> 00:05:38,187 in the circuit. And we'll see how that works when we take 94 00:05:38,187 --> 00:05:43,370 a look at our full diagram again. And this is a Resistor. 95 00:05:43,370 --> 00:05:45,713 Now we haven't actually talked about resistors yet. 96 00:05:45,713 --> 00:05:48,278 But they're the most common circuit elements, and in order to have an 97 00:05:48,278 --> 00:05:51,203 interesting circuit diagram, we kind of want to have some Resistors thrown in 98 00:05:51,203 --> 00:05:54,295 there. We'll talk a little bit more in 99 00:05:54,295 --> 00:05:57,055 subsequent classes about exactly what these Resistors mean. 100 00:05:57,055 --> 00:06:00,410 Resistors are drawn by drawing zig-zag lines. 101 00:06:00,410 --> 00:06:03,930 Now the number of zigs and zags varies, and it's not particularly important. 102 00:06:03,930 --> 00:06:08,960 If you see something with the going up and down zig and zag, it's a Resistor. 103 00:06:08,960 --> 00:06:12,428 Other similar devices will be presented and introduced as we encounter them, but 104 00:06:12,428 --> 00:06:15,845 basically, this is just kind of a passive device, it doesn't have any specified, 105 00:06:15,845 --> 00:06:19,262 known voltage or current, it's completely at the at the system as to what it's 106 00:06:19,262 --> 00:06:26,630 values are going to be. This is Ground. 107 00:06:26,630 --> 00:06:30,710 It's, identified by showing a series of parallel lines getting decreasingly 108 00:06:30,710 --> 00:06:34,368 smaller. Ground kind of gives us a point of 109 00:06:34,368 --> 00:06:36,845 reference, when we're talking about voltage. 110 00:06:36,845 --> 00:06:39,900 You remember from the voltage lecture, we talked about how important it was to 111 00:06:39,900 --> 00:06:43,760 know, with respect to what, when we talked about voltage. 112 00:06:43,760 --> 00:06:46,630 Well with Ground, it kind of gives us a zero. 113 00:06:46,630 --> 00:06:50,480 sea level per voltage as it were. Where we say, this is going to be our 114 00:06:50,480 --> 00:06:53,060 threshold, and everything has it in common. 115 00:06:53,060 --> 00:06:55,235 Now, sometimes Ground is actually a physical thing. 116 00:06:55,235 --> 00:06:58,390 You might know lightning rods use a Ground. 117 00:06:58,390 --> 00:07:02,225 It's a wire that goes from a point of a building into the physical ground giving 118 00:07:02,225 --> 00:07:05,824 path for electrons to flow, without having the electrons go through your 119 00:07:05,824 --> 00:07:10,872 house and cause damage. Sometimes you can use something like a 120 00:07:10,872 --> 00:07:13,908 Grounding strap, that would allow the electrons to flow through the Grounding 121 00:07:13,908 --> 00:07:17,930 strap, rather than through some kind of sensitive device. 122 00:07:17,930 --> 00:07:22,346 In these circumstances, this is actually a real ground that is some physical 123 00:07:22,346 --> 00:07:24,884 thing. In our circuit diagrams though, 124 00:07:24,884 --> 00:07:28,740 generally, we're just using it as a point of reference of what is zero voltage. 125 00:07:28,740 --> 00:07:32,252 What do we mean by zero? Now we're going to talk a little bit 126 00:07:32,252 --> 00:07:36,272 about open and short circuits. You hear the term short circuit thrown 127 00:07:36,272 --> 00:07:39,170 around a lot. Something, some device breaks, they often 128 00:07:39,170 --> 00:07:41,880 say oh, well there, there was a short circuit. 129 00:07:41,880 --> 00:07:44,496 Something went bad. Well, this is what these things actually 130 00:07:44,496 --> 00:07:46,570 mean. An open circuit is where we have some 131 00:07:46,570 --> 00:07:50,360 devices where, the two terminals are not connected to anything. 132 00:07:50,360 --> 00:07:54,328 There's no path, for anything to flow. And because it's a circuit, there 133 00:07:54,328 --> 00:07:59,160 probably needs to be a closed loop, in order for anything interesting to happen. 134 00:07:59,160 --> 00:08:01,910 So if we have an open circuit, we just have some dangling ends. 135 00:08:01,910 --> 00:08:04,550 Normally we're going to use these open circles to identify that it's not 136 00:08:04,550 --> 00:08:08,322 connected to anything. Now, sometimes we'll take a measurement 137 00:08:08,322 --> 00:08:11,586 across an open circuit, but we don't see it, any current flowing, so electrically 138 00:08:11,586 --> 00:08:16,040 it's not very important. This is a short circuit. 139 00:08:16,040 --> 00:08:18,840 If we in turn take two points of the circuit element and connect them 140 00:08:18,840 --> 00:08:23,960 together, now current can flow like this, without going through this device. 141 00:08:23,960 --> 00:08:27,038 The reason we often talk about when things break, there being a short 142 00:08:27,038 --> 00:08:31,559 circuit, is that when this happens, usually bad things are happening. 143 00:08:31,559 --> 00:08:34,640 Things are, currents are going where they're not supposed to. 144 00:08:34,640 --> 00:08:37,130 Voltages are not what we expect them to be. 145 00:08:37,130 --> 00:08:40,165 And so that's why often short circuit means that something broke. 146 00:08:40,165 --> 00:08:43,633 But in practice, actually short circuit just means that we are connecting the two 147 00:08:43,633 --> 00:08:47,500 terminals at some device together. Using a wire. 148 00:08:50,040 --> 00:08:53,395 These circuits, are what we call self-contradictory, or they don't make 149 00:08:53,395 --> 00:08:56,235 sense. Remember, that voltage sources specify 150 00:08:56,235 --> 00:09:00,340 what a voltage is, and it's constant. And, we know what it is, it doesn't 151 00:09:00,340 --> 00:09:04,306 depend on the circuit. And, we know that wires have zero voltage 152 00:09:04,306 --> 00:09:07,246 across them, so if we look at this circuit on the left, the voltage source 153 00:09:07,246 --> 00:09:11,225 says that we have five volts from the top to the bottom. 154 00:09:11,225 --> 00:09:14,620 And the wire says we have zero volts from the top to the bottom. 155 00:09:14,620 --> 00:09:16,780 Which one is it? Well, it can't really be either. 156 00:09:16,780 --> 00:09:19,880 It's self-contradictory. It doesn't make sense. 157 00:09:19,880 --> 00:09:22,625 But you might be wondering, it's real easy to connect a wire to the sides of 158 00:09:22,625 --> 00:09:25,210 the battery. That's not hard to do at all. 159 00:09:25,210 --> 00:09:28,732 So why can't we make this? Well, when we actually do that, you might 160 00:09:28,732 --> 00:09:31,070 notice that the wire gets really, really hot. 161 00:09:31,070 --> 00:09:34,710 And the battery loses it's power really, really quickly. 162 00:09:34,710 --> 00:09:38,004 What is actually going on is, the wire is no longer acting like a wire in the 163 00:09:38,004 --> 00:09:41,500 circuit diagram. It's starting to act like a circuit 164 00:09:41,500 --> 00:09:44,452 element itself. So when we have a diagram that's 165 00:09:44,452 --> 00:09:47,780 self-contradictory, it means that we're missing some kind of mathematical 166 00:09:47,780 --> 00:09:51,160 assumption, its not very accurate, and we're going to modify the circuit to be 167 00:09:51,160 --> 00:09:56,475 more representative of the real system. And when we look at the one on the right, 168 00:09:56,475 --> 00:09:59,625 the current source says that we have one Amp of current flowing, but flowing 169 00:09:59,625 --> 00:10:02,745 where? There's no way for the current to go, 170 00:10:02,745 --> 00:10:07,760 because the circuit is an open circuit. The current's stuck, it's not closed. 171 00:10:07,760 --> 00:10:12,150 So again, it's self-contradictory. So when we put it all together, we can 172 00:10:12,150 --> 00:10:15,322 see all of the devices here, put together one big diagram, here we have our 173 00:10:15,322 --> 00:10:18,858 resistor, we have an independent voltage source here and we specify its voltage, 174 00:10:18,858 --> 00:10:24,640 VS, for Voltage Source. Here we have an independent current 175 00:10:24,640 --> 00:10:28,357 source, its current Is is specified, R2, R3, here we have a nice little short 176 00:10:28,357 --> 00:10:32,133 circuit, where we've connected the two ends of this resister, here's an open 177 00:10:32,133 --> 00:10:35,968 circuit, where we're actually taking a measurement of the voltage across it, 178 00:10:35,968 --> 00:10:42,710 here's a dependant current source, and its value is G1 times Va. 179 00:10:42,710 --> 00:10:45,720 So we've measured a voltage here, and we're multiplying it by some G. 180 00:10:45,720 --> 00:10:47,743 If we look down here, we can see where G is. 181 00:10:47,743 --> 00:10:53,449 In this case, G1 is 0.005 Amps per volt. And we have to have this Amps per volt, 182 00:10:53,449 --> 00:10:57,048 because this is a voltage, but we know this source has to be in a current, or 183 00:10:57,048 --> 00:11:00,708 Amps. So we have to do the proper. 184 00:11:00,708 --> 00:11:05,870 Division of Amps per volt here. Here G2 is 1000 volts per Amp. 185 00:11:05,870 --> 00:11:09,042 Again, volts per Amp allowing us to get something in the result that's in a 186 00:11:09,042 --> 00:11:12,630 voltage, even though we're multiplying by a current. 187 00:11:15,160 --> 00:11:17,640 It's possible for us to actually manipulate circuits, to change them into 188 00:11:17,640 --> 00:11:20,414 some different circuit. And this is a particularly confusing 189 00:11:20,414 --> 00:11:22,770 circuit. It's kind of hard to follow. 190 00:11:22,770 --> 00:11:25,101 We notice there are junctions, some places where there are dots, but we also 191 00:11:25,101 --> 00:11:28,310 see that there are some wires that cross. And there are no dots. 192 00:11:28,310 --> 00:11:32,740 They're not connected together. They just happen to overlap each other. 193 00:11:32,740 --> 00:11:35,555 So this circuit might be really difficult for us to analyze. 194 00:11:35,555 --> 00:11:38,397 So let's try moving it around and change it up, to get something that's 195 00:11:38,397 --> 00:11:41,515 equivalent, and maybe easier for us to analyze. 196 00:11:41,515 --> 00:11:44,760 To make it a little bit easier to see, I colored the nodes. 197 00:11:45,820 --> 00:11:48,920 So we'll notice that here, we have this blue node that covers a lot of area in 198 00:11:48,920 --> 00:11:53,420 the circuit, cover, connects a whole lot of different devices. 199 00:11:53,420 --> 00:11:58,510 Let's have a red node, a green node and a pink node. 200 00:11:58,510 --> 00:12:01,047 And so let's take a look at one particular device, and see how things are 201 00:12:01,047 --> 00:12:04,770 connected together. Device A, which is just a square 202 00:12:04,770 --> 00:12:10,190 representing some unknown device, is connecting the red and the blue nodes. 203 00:12:11,560 --> 00:12:14,269 So we know that any circuit that is going to be equivalent to this, has to have 204 00:12:14,269 --> 00:12:21,121 that same behavior. So this would be an equivalent circuit. 205 00:12:21,121 --> 00:12:26,860 A, here, connects the red node to the blue node, everything's okay. 206 00:12:26,860 --> 00:12:30,040 And in turn if we go through each of these individual devices, B goes from 207 00:12:30,040 --> 00:12:34,760 blue to pink, so B from blue to pink. H from pink to blue, H from pink to blue. 208 00:12:34,760 --> 00:12:37,945 If you go through, you'll verify that each of these devices is connected to the 209 00:12:37,945 --> 00:12:41,888 same two nodes. So although somethings are different, the 210 00:12:41,888 --> 00:12:45,220 basic behavior of the system remains the same. 211 00:12:45,220 --> 00:12:48,730 It is a little bit important to notice, however, that if there is a current that 212 00:12:48,730 --> 00:12:54,260 we're measuring across a wire, we might lose it by doing this change. 213 00:12:54,260 --> 00:12:59,020 For example, if we look at the wire between this E and this G, it has no 214 00:12:59,020 --> 00:13:06,090 corresponding wire in this diagram because everything here. 215 00:13:06,090 --> 00:13:08,440 Just kind of bridges up to the same junction point. 216 00:13:08,440 --> 00:13:11,885 So, that's one thing to pay attention to, but as long as you're not caring about 217 00:13:11,885 --> 00:13:16,360 certain values that cross wires, doing this is not a problem at all. 218 00:13:16,360 --> 00:13:19,605 If you find a way of being able to distribute a system in a different way, 219 00:13:19,605 --> 00:13:23,015 where everything is still connected in the same manner, same two nodes are 220 00:13:23,015 --> 00:13:26,345 connected. Then that's perfectly fine, you can alter 221 00:13:26,345 --> 00:13:31,034 it as much as you like. So to summarize we described the concept 222 00:13:31,034 --> 00:13:34,425 of a node and how to identify one. We introduced independent and dependent 223 00:13:34,425 --> 00:13:37,746 voltage and current sources, as well as the dependent varieties. 224 00:13:37,746 --> 00:13:40,989 We introduced the resistor but we didn't describe how it behaves, because that's a 225 00:13:40,989 --> 00:13:44,870 topic for a later lecture. We presented the idea of a ground. 226 00:13:44,870 --> 00:13:48,040 And we showed some examples of circuits that are self-contradictory. 227 00:13:48,040 --> 00:13:51,538 They don't really make sense. And really what that means is that your 228 00:13:51,538 --> 00:13:54,576 system that you've diagrammed is not really representative of the actual 229 00:13:54,576 --> 00:13:59,299 system that you're looking at. And we've described how two circuits can 230 00:13:59,299 --> 00:14:03,310 be equivalent as far as a circuit's view's concerned. 231 00:14:03,310 --> 00:14:05,619 Just by moving things around. So as long as everything is still 232 00:14:05,619 --> 00:14:08,865 connected in the same way. For our next class, we will see another 233 00:14:08,865 --> 00:14:12,585 way that voltages and currents relate, as well as how charges move through 234 00:14:12,585 --> 00:14:15,913 materials. And if there is anything that you were, 235 00:14:15,913 --> 00:14:18,949 found confusing in this class or you have any questions about the material that was 236 00:14:18,949 --> 00:14:22,680 covered here, again I remind you to go to the forums. 237 00:14:22,680 --> 00:14:25,432 Ask questions there, and then, either your students or, fellow students, or 238 00:14:25,432 --> 00:14:28,790 Doctor Ferri, or I, will be able to answer your questions there. 239 00:14:28,790 --> 00:14:31,877 Look forward to seeing you again next time in our next module, where we start 240 00:14:31,877 --> 00:14:35,850 talking about some resistance circuits. Until then, cheers.