1 00:00:00,000 --> 00:00:05,430 2 00:00:05,430 --> 00:00:07,510 PROFESSOR: Today I'd like to talk to you about a new method 3 00:00:07,510 --> 00:00:08,790 for solving circuits. 4 00:00:08,790 --> 00:00:12,520 Last time, we reviewed using KVL, KCL, and Ohm's Law in 5 00:00:12,520 --> 00:00:14,780 order to solve circuits in a general sense. 6 00:00:14,780 --> 00:00:17,060 This produced a lot of equations, in particular, a 7 00:00:17,060 --> 00:00:19,530 lot of redundant equations or a lot of dependent equations, 8 00:00:19,530 --> 00:00:23,090 that we don't necessarily need for solving our circuit. 9 00:00:23,090 --> 00:00:26,880 Today I'm going to review the Node Voltage Component Current 10 00:00:26,880 --> 00:00:29,135 method, which is very similar to node analysis. 11 00:00:29,135 --> 00:00:32,390 So if you hear one versus the other, know that you're 12 00:00:32,390 --> 00:00:34,030 talking about approximately the same thing. 13 00:00:34,030 --> 00:00:35,960 And I'll review the difference in a second. 14 00:00:35,960 --> 00:00:38,520 Once we know how to use the NVCC method for solving 15 00:00:38,520 --> 00:00:43,360 circuits, we can express the relationships between 16 00:00:43,360 --> 00:00:46,370 components in our circuit more concisely and more 17 00:00:46,370 --> 00:00:49,150 effectively, and possibly solve our equations faster, 18 00:00:49,150 --> 00:00:51,825 which is relevant when we're working on a mid-term or in 19 00:00:51,825 --> 00:00:54,680 the general sense, just trying to save time. 20 00:00:54,680 --> 00:00:55,930 Let's take a look at NVCC. 21 00:00:55,930 --> 00:01:00,587 22 00:01:00,587 --> 00:01:03,370 As I said before NVCC, stands for Node 23 00:01:03,370 --> 00:01:04,940 Voltage Component Current. 24 00:01:04,940 --> 00:01:07,990 And what that means is if you have a very simple circuit-- 25 00:01:07,990 --> 00:01:12,690 let's say just a voltage source 26 00:01:12,690 --> 00:01:13,940 and a couple of resistors. 27 00:01:13,940 --> 00:01:22,500 28 00:01:22,500 --> 00:01:27,030 Previously, with KVL, we were interested in the voltage drop 29 00:01:27,030 --> 00:01:29,380 around the loop being equivalent to 0. 30 00:01:29,380 --> 00:01:33,370 In this case, we're actually going to look at the voltages 31 00:01:33,370 --> 00:01:34,795 associated with particular nodes. 32 00:01:34,795 --> 00:01:37,490 33 00:01:37,490 --> 00:01:42,030 To do that we're going to label our nodes, which are 34 00:01:42,030 --> 00:01:43,465 anywhere our components connect. 35 00:01:43,465 --> 00:01:50,150 36 00:01:50,150 --> 00:01:54,740 We're also going to go after the component current. 37 00:01:54,740 --> 00:01:57,740 When we're doing KCL, we typically look at the flow in 38 00:01:57,740 --> 00:01:59,420 and out of a particular node. 39 00:01:59,420 --> 00:02:01,820 At this point, we're going to look at the flow through a 40 00:02:01,820 --> 00:02:02,650 given component. 41 00:02:02,650 --> 00:02:06,110 So we're also going to label all of the currents associated 42 00:02:06,110 --> 00:02:08,289 with our circuit. 43 00:02:08,289 --> 00:02:10,370 But when we approach NVCC method, we're going to think 44 00:02:10,370 --> 00:02:15,020 about the currents flowing through a particular component 45 00:02:15,020 --> 00:02:18,100 as opposed to and out of a particular node. 46 00:02:18,100 --> 00:02:23,610 NVCC is sort of the opposite of KVL and KCL in that sense, 47 00:02:23,610 --> 00:02:25,490 even though you're still going to end up using the same 48 00:02:25,490 --> 00:02:26,740 relationships. 49 00:02:26,740 --> 00:03:09,500 50 00:03:09,500 --> 00:03:13,830 So at this point, I've labeled the currents going through-- 51 00:03:13,830 --> 00:03:16,780 I labeled one individual current for every component in 52 00:03:16,780 --> 00:03:18,030 my circuit. 53 00:03:18,030 --> 00:03:22,140 54 00:03:22,140 --> 00:03:24,450 The next step would be to identify what I'm going to 55 00:03:24,450 --> 00:03:28,520 call ground, or in particular, one of my nodes -- 56 00:03:28,520 --> 00:03:31,740 I'm going to assign to ground or relative voltage 0. 57 00:03:31,740 --> 00:03:34,600 At that point, I'm going to write out the relationships 58 00:03:34,600 --> 00:03:39,050 between the voltage drop across particular components, 59 00:03:39,050 --> 00:03:42,460 the current flowing through that particular component, and 60 00:03:42,460 --> 00:03:49,090 whatever relationship the component requires the voltage 61 00:03:49,090 --> 00:03:50,920 and the current to have to one another. 62 00:03:50,920 --> 00:03:54,930 63 00:03:54,930 --> 00:03:59,340 That's a whirlwind review of NVCC method. 64 00:03:59,340 --> 00:04:02,870 Node analysis is very similar. 65 00:04:02,870 --> 00:04:05,840 The main difference between node analysis and NVCC method 66 00:04:05,840 --> 00:04:09,720 is when your component is a voltage source. 67 00:04:09,720 --> 00:04:12,840 And there are multiple currents flowing into that 68 00:04:12,840 --> 00:04:15,500 voltage source. 69 00:04:15,500 --> 00:04:17,870 You can treat this as a single voltage. 70 00:04:17,870 --> 00:04:24,330 You can treat this as a single voltage node, where this 71 00:04:24,330 --> 00:04:27,140 voltage it has value 0. 72 00:04:27,140 --> 00:04:35,710 And actually write your KCL equations as though this point 73 00:04:35,710 --> 00:04:38,450 were collapsed. 74 00:04:38,450 --> 00:04:43,010 So current flowing in and current flowing out, or vice 75 00:04:43,010 --> 00:04:45,580 versa, have to sum to 0. 76 00:04:45,580 --> 00:04:47,470 That's the major difference. 77 00:04:47,470 --> 00:04:48,720 Let's look at an example. 78 00:04:48,720 --> 00:04:52,340 79 00:04:52,340 --> 00:04:54,110 You can find this example repeated in 80 00:04:54,110 --> 00:04:57,680 6.4.3 of the reading. 81 00:04:57,680 --> 00:05:01,940 And I'm going to walk through these directions. 82 00:05:01,940 --> 00:05:03,910 So the first thing I'm going to do is label my 83 00:05:03,910 --> 00:05:05,160 nodes and my currents. 84 00:05:05,160 --> 00:05:15,230 85 00:05:15,230 --> 00:05:17,330 People interchangeably use e or n. 86 00:05:17,330 --> 00:05:18,580 It doesn't really matter. 87 00:05:18,580 --> 00:05:24,970 88 00:05:24,970 --> 00:05:27,420 I guess n in particular could refer to the node, while e in 89 00:05:27,420 --> 00:05:29,580 particular could refer to the voltage 90 00:05:29,580 --> 00:05:30,830 associated with that node. 91 00:05:30,830 --> 00:05:55,200 92 00:05:55,200 --> 00:05:57,610 Now I'm going to specify the voltage drop across a 93 00:05:57,610 --> 00:05:59,720 particular component in terms of the node voltages. 94 00:05:59,720 --> 00:06:06,670 95 00:06:06,670 --> 00:06:11,990 I'm also going to assign n0 to 0 as my ground. 96 00:06:11,990 --> 00:06:16,070 As a consequence, I know that n1 is going to be 15 Volts. 97 00:06:16,070 --> 00:06:23,750 98 00:06:23,750 --> 00:06:30,290 My voltage drop is typically specified in the same 99 00:06:30,290 --> 00:06:36,800 direction as the current - that I've also decided. 100 00:06:36,800 --> 00:06:40,710 So this convention is arbitrary. 101 00:06:40,710 --> 00:06:44,140 But if you want to be consistent in your work, and 102 00:06:44,140 --> 00:06:46,490 make it easier to get partial credit or get help in office 103 00:06:46,490 --> 00:06:50,570 hours, et cetera, then assume that the voltage drop occurs 104 00:06:50,570 --> 00:06:52,090 in the same direction as the current. 105 00:06:52,090 --> 00:07:31,390 106 00:07:31,390 --> 00:07:34,800 That's it for our relationship associated with voltage drop. 107 00:07:34,800 --> 00:07:40,930 Now I'm going to go over KCL for the relevant nodes. 108 00:07:40,930 --> 00:07:43,660 And in the last step I'm going to combine the two into the 109 00:07:43,660 --> 00:07:49,280 equation that you're certainly allowed to use to express your 110 00:07:49,280 --> 00:07:51,440 work on midterms. 111 00:07:51,440 --> 00:07:53,720 Or if you can skip to the third step 112 00:07:53,720 --> 00:07:55,540 immediately, then that's OK. 113 00:07:55,540 --> 00:07:57,840 Just check your signs. 114 00:07:57,840 --> 00:07:59,090 Here's the second step. 115 00:07:59,090 --> 00:08:02,450 116 00:08:02,450 --> 00:08:05,370 Flowing into n1 is i0 and flowing out is i1. 117 00:08:05,370 --> 00:08:12,530 118 00:08:12,530 --> 00:08:15,410 So i0 is going to be equal to i1. 119 00:08:15,410 --> 00:08:19,040 Flowing into n2 is i1 and i3. 120 00:08:19,040 --> 00:08:20,700 And flowing out of n2 is i2. 121 00:08:20,700 --> 00:08:35,520 122 00:08:35,520 --> 00:08:42,020 Flowing into n0 is i2, and flowing out of 123 00:08:42,020 --> 00:08:45,710 n0 is i0 and i3. 124 00:08:45,710 --> 00:08:46,900 we're almost certainly not going to end 125 00:08:46,900 --> 00:08:47,810 up using that equation. 126 00:08:47,810 --> 00:08:50,680 Because it's the last of our KCL equations and is dependent 127 00:08:50,680 --> 00:08:52,230 upon the other equations that we've already 128 00:08:52,230 --> 00:08:53,480 written out for KCL. 129 00:08:53,480 --> 00:09:05,660 130 00:09:05,660 --> 00:09:07,070 I3 is equal to 10 Amperes. 131 00:09:07,070 --> 00:09:18,520 132 00:09:18,520 --> 00:09:19,865 So we can go ahead and make that substitution. 133 00:09:19,865 --> 00:09:27,140 134 00:09:27,140 --> 00:09:30,860 I still have to work with i1 and i2 though. 135 00:09:30,860 --> 00:09:33,320 And I can go after expressions for them in terms of my node 136 00:09:33,320 --> 00:09:37,980 voltages and components by using the equations for 137 00:09:37,980 --> 00:09:39,510 voltage drop I made earlier. 138 00:09:39,510 --> 00:10:30,500 139 00:10:30,500 --> 00:10:34,120 This is the equation that you can jump straight to, if you 140 00:10:34,120 --> 00:10:38,340 understand where this expression comes from, as a 141 00:10:38,340 --> 00:10:44,555 consequence, of our KCL and also our component voltages. 142 00:10:44,555 --> 00:10:53,770 143 00:10:53,770 --> 00:10:57,030 I'm going to substitute in 15 Volts for n1 here. 144 00:10:57,030 --> 00:11:05,640 145 00:11:05,640 --> 00:11:09,710 And now I have an expression that only contains n2 and 146 00:11:09,710 --> 00:11:10,870 known values. 147 00:11:10,870 --> 00:11:12,720 So I can solve for n2. 148 00:11:12,720 --> 00:11:15,750 and I'll do that real quickly right now. 149 00:11:15,750 --> 00:11:17,360 So first I'm just going to copy this over. 150 00:11:17,360 --> 00:11:35,730 151 00:11:35,730 --> 00:11:37,270 I'm going to multiply through by 6 Ohms. 152 00:11:37,270 --> 00:12:15,880 153 00:12:15,880 --> 00:12:20,270 And I solved for the voltage associated with n2. 154 00:12:20,270 --> 00:12:34,180 At this point, I can solve for i2 and i1. 155 00:12:34,180 --> 00:12:43,040 156 00:12:43,040 --> 00:12:44,290 Sorry about that. 157 00:12:44,290 --> 00:12:49,958 158 00:12:49,958 --> 00:12:51,730 What do I have left? 159 00:12:51,730 --> 00:12:54,390 i3 I know is 10 Amperes. 160 00:12:54,390 --> 00:12:57,015 i0 is equal to i1, which is negative 1 Amperes. 161 00:12:57,015 --> 00:13:07,070 162 00:13:07,070 --> 00:13:11,660 There's a voltage drop associated with the 3 Ohm 163 00:13:11,660 --> 00:13:19,060 resistor, which is 15 minus 18, negative 3 Volts. 164 00:13:19,060 --> 00:13:28,541 165 00:13:28,541 --> 00:13:30,950 And the voltage drop associated with the 2 Ohm 166 00:13:30,950 --> 00:13:36,190 resistor is 18 Volts, since n0 is ground. 167 00:13:36,190 --> 00:13:40,860 This concludes my introduction to node voltage component 168 00:13:40,860 --> 00:13:44,470 current method or node analysis without the ability 169 00:13:44,470 --> 00:13:49,510 to collapse voltage sources for KCL. 170 00:13:49,510 --> 00:13:50,760