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481740, + 484970, + 487140 + ], + "text": [ + "INSTRUCTOR: Based on the previous method or the", + "previous property that you saw for linear circuits, we are", + "now ready to define the superposition method for", + "circuit analysis.", + "Note that the superposition method", + "applies to linear circuits.", + "And again, to refresh your memory, remember, we are in", + "the EECS playground that we got into by adhering to the", + "lumped matter discipline.", + "And within that, we looked at the node method and the KVL", + "KCL method that applies all over the EECS playground.", + "And then what we'll now do is look at some methods that will", + "apply to only a region of this playground where linear", + "circuits reside.", + "So the first of these methods is the superposition method.", + "And again, it applies to linear circuits.", + "So the method is very simple and inspired by the", + "superposition property that we studied for linear circuits.", + "So the method simply says this.", + "You first find the responses of the circuit to each source", + "acting alone.", + "Think of this as a divide and conquer method where you take", + "your entire circuit, and you find the responses of the", + "circuit to each source acting alone.", + "You turn off all the sources, and you find the response to", + "each source acting alone.", + "Then what you do is simply sum those individual responses.", + "Note that this technique applies to", + "independent sources only.", + "So if I have a linear circuit, then this technique applies to", + "independent sources only.", + "Now we will look at what happens when you have", + "dependent sources and so on in later lectures.", + "OK, let's move ahead.", + "The first step was find the response of the circuit to", + "each source acting alone.", + "But what does it mean for each source to act alone?", + "What it means is that you turn off all the other sources.", + "So for example, suppose we are focused on a", + "voltage source here.", + "What does it mean to turn off this voltage source?", + "In other words, if I want to set this voltage to 0, what", + "does it mean in terms of my circuit?", + "So in terms of my circuit, what this means is that I am", + "going to short the source.", + "So what you do is you short the source, and you end up", + "with a short circuit here.", + "And that is my voltage source having been set to 0.", + "And so I take all my voltage sources in the circuit and", + "simply short them out.", + "And this would be making each of the sources to act alone.", + "OK, next let's look at a current source and see what it", + "means to set a current source to 0.", + "So in this case, what you do is much as you set a voltage", + "source to 0 by shorting it out, you set the current", + "source to 0 by open-circuiting it like so.", + "So you create an open circuit in place of the current", + "source, and that's what it means to set a", + "current source to zero.", + "OK, so now we are ready to go try out an example using the", + "method of superposition.", + "And again, remember the method of superposition has", + "two parts to it.", + "In the first part, you find the responses of the circuit", + "to each source acting alone.", + "And then second, you sum up the partial responses.", + "So let's go back to our old faithful example.", + "In this example, we have two sources, a voltage source and", + "a current source.", + "And let's say our goal is to find the node voltage e taken", + "with respect to this ground.", + "And we are going to use the superposition", + "method to do the circuit.", + "So I showed the circuit on the right-hand corner here.", + "And notice that e is the node voltage that I", + "need to figure out.", + "So by the superposition method, I have two steps.", + "My first step is find the responses of the circuit to", + "each source acting alone.", + "So what I'm going to do is let me start with finding the", + "response of the circuit to the voltage source acting alone.", + "So what do I do to get a subcircuit in which the", + "voltage source is acting alone?", + "So I want you to think about this and try to figure out", + "what the resulting subcircuit is going to look like.", + "I'll give you a few seconds to do that before I do it myself.", + "All right.", + "This is the subcircuit.", + "And what I've done here is I've had to turn the current", + "source off.", + "So notice that out here I create an open circuit, and", + "that is the result of my current source", + "being turned off.", + "And this is my usual ground node.", + "And let me call this node voltage with the voltage", + "source acting alone as ev. So ev is the partial response of", + "the circuit to the voltage source acting alone.", + "Now how do we go about solving for ev?", + "Notice that we have a known pattern here.", + "We have a voltage source connected to a pair of", + "resistors, R1 and R2.", + "And ev is simply the voltage across R2.", + "Now this is a known pattern.", + "So one thing you should keep in mind is that in circuits", + "and electronics, we use patterns a lot.", + "Whenever we see a pattern, we can directly go and write down", + "the what the outward response is going to look like.", + "What I'm going to do is throughout this course, as you", + "we more and more patterns, I am going to alert", + "you to these patterns.", + "So right here is a voltage divider pattern.", + "So for the voltage divider pattern, I can write down ev", + "as being some fraction of the source voltage v. But the", + "divider action is simply R2 divide by R2 plus R2.", + "So it is simply the voltage across R2, and that is given", + "by R2 divide by R1 plus R2.", + "And this is a known pattern that you will find very", + "helpful as you analyze circuits very quickly.", + "Next let's look at I acting alone.", + "Before we do that, what do we have so far?", + "Again, recall, this is the circuit we", + "are trying to analyze.", + "We are trying to get the node voltage e.", + "And so far we have computed the partial voltage ev due to", + "the voltage source acting alone.", + "As the next step-- again, this is still step one of the", + "superposition method--", + "let's look at the partial response of the circuit due to", + "the current acting alone.", + "To get the response for the current acting alone, I need", + "to build a circuit in which the voltage", + "source is turned off.", + "I'll let you think for a couple of seconds as to what", + "the circuit will look like before I draw it out for you.", + "OK, let's go ahead.", + "So to turn off this voltage source, all I have to do is", + "replace it with a short circuit like so.", + "So notice that I have replaced the voltage source with a", + "short circuit, and I've left the current source in place.", + "I have my ground node here.", + "And notice that my goal is to find the partial voltage eI", + "that is a result of the current source acting alone.", + "So notice that I have a second pattern here.", + "And in this case, this is a current divider pattern.", + "Actually, this is a even simpler pattern.", + "I simply have a current that is flowing", + "into a pair of resistors.", + "OK, so I have a current, I, that is flowing into a pair of", + "resistors, R1 and R2.", + "And so I can compute the voltage across the pair of", + "resistors very straightforwardly.", + "So eI is simply the resistance times the current.", + "And the resistance of a paralel pair of resistors is", + "simply R1 R2 divide by R1 plus R2 times the current I.", + "OK, so now I have computed both ev and eI, the two", + "partial voltages with each of the voltages acting alone.", + "And now I am ready for step two of the", + "superposition method.", + "And the step two of the superposition method simply", + "says that you sum the two partial voltages, ev and eI.", + "So my resulting voltage e is simply the sum of the two", + "partial voltages ev and eI.", + "And I have those as R2 divide by R1 plus R2 times v. And I", + "sum that to eI.", + "And eI is R1 R2 divide by R1 plus R2 times I. And", + "there you have it.", + "Not surprisingly, this expression here is identical", + "to the expression that you obtained by using the node", + "method in the previous lecture." + ] +} \ No newline at end of file diff --git a/subs/227NDapJIz0.srt.sjson b/subs/227NDapJIz0.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/227NDapJIz0.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/6nj1OCvSRI8.srt.sjson b/subs/6nj1OCvSRI8.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/6nj1OCvSRI8.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/7ssVrey04Pw.srt.sjson b/subs/7ssVrey04Pw.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/7ssVrey04Pw.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/9bAUDWtsUkE.srt.sjson b/subs/9bAUDWtsUkE.srt.sjson new file mode 100644 index 0000000000..ee71e27a5d --- /dev/null +++ b/subs/9bAUDWtsUkE.srt.sjson @@ -0,0 +1,398 @@ +{ + "start": [ + 210, + 2420, + 5570, + 8930, + 12530, + 15130, + 18320, + 21090, + 22930, + 27010, + 27710, + 32770, + 37620, + 40130, + 41820, + 43850, + 48330, + 50890, + 52750, + 55680, + 57920, + 62680, + 65880, + 69760, + 71690, + 73260, + 76960, + 79730, + 82400, + 84210, + 88000, + 89370, + 91940, + 95090, + 98650, + 100600, + 101680, + 107170, + 108370, + 113180, + 116660, + 119100, + 122830, + 125730, + 130509, + 131910, + 135140, + 138390, + 140890, + 143820, + 146880, + 149460, + 151750, + 155890, + 156540, + 159790, + 161890, + 167170, + 171160, + 177815, + 179510, + 182280, + 183920, + 188130, + 189530, + 193470, + 197510, + 201245, + 204430, + 208956, + 213830, + 214780, + 217640, + 219770, + 224350, + 226850, + 230110, + 232610, + 235270, + 236520, + 241170, + 244200, + 247150, + 249260, + 252150, + 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171160, + 177815, + 179510, + 182280, + 183920, + 188130, + 189530, + 193470, + 197510, + 201245, + 204430, + 208956, + 213830, + 214780, + 217640, + 219770, + 224350, + 226850, + 230110, + 232610, + 235270, + 236520, + 241170, + 244200, + 247150, + 249260, + 252150, + 256800, + 260240, + 262470, + 266330, + 267860, + 271280, + 274920, + 277880, + 279710, + 281760, + 285160, + 289220, + 292680, + 296890, + 298490, + 303230, + 306510, + 308777, + 311650, + 315870, + 320940, + 324050, + 326490, + 328780, + 331280, + 332820, + 335400, + 338620, + 341430, + 345500, + 348630, + 352335, + 355910, + 359730, + 363180, + 365400, + 369220, + 372480, + 377750, + 381520, + 384570, + 388780, + 391360, + 392440, + 396330, + 397580 + ], + "text": [ + "PROFESSOR: In the previous segment, we saw that circuits", + "composed of linear elements were, themselves, linear.", + "In this segment, we will see that linear circuits or linear", + "systems can be analyzed with extremely powerful techniques.", + "We will study two of these properties of circuits,", + "homogeneity and superposition, in this segment.", + "Let's start by studying the property of homogeneity.", + "So what does homogeneity mean?", + "Supposing we have a system with a bunch of inputs one", + "output here.", + "And let's say the inputs are x1, x2, and so on.", + "And for these xes let's say the corresponding output is y.", + "Let me add a little cartoon here, just to", + "make it easy to follow.", + "As they say, a picture is worth 1,000 words.", + "So let's say, if you have apple as an input and you get", + "a different kind of apple as an output, then let's look at", + "what the property of homogeneity says.", + "If I take the same system and if I", + "multiply each of the inputs--", + "x1, x2, and the old output, y-- if I multiply each of the", + "inputs with some constant, alpha, then the property of", + "homogeneity says that the output will also be multiplied", + "by the same value, alpha.", + "So this is the homogeneity property.", + "And in terms of our picture, if you have an Apple and you", + "took a fraction of the apple out, then your output would", + "also have the same fraction of the apple out.", + "So this is the homogeneity property.", + "Next let's look at another extremely powerful technique,", + "superposition.", + "Now superposition is a property of linear circuits,", + "and let's first understand what this property means.", + "So supposing I have a system here.", + "And what I'll do is I'll apply two sets of", + "inputs to the system.", + "So in the first set, let's say I apply the a set of inputs,", + "x1a, x2a, and so on.", + "And let's say that that gives rise to the a set of outputs.", + "And then if I take the same system--", + "just to make it clear, let me mark it as s.", + "If I take the same system and I apply a b set of inputs--", + "so x1b, x2b, and so on--", + "and if I get a corresponding output, yb, then what can we", + "say about the resulting system?", + "And just to make it very clear, going back to our", + "pictures and cartoons here, let's say the a set of inputs", + "corresponds to apples, a for apples.", + "And the b set of inputs goes on to blueberries.", + "So jokingly here, if I feed a bunch of apples to the system", + "and I get applesauce at the output, and on the other hand,", + "if I feed a bunch of blueberries to the system and", + "I get blueberry sauce at the output, then let's do some fun", + "stuff here.", + "Suppose I take the same system and I feed through the system", + "the sum of both of these inputs.", + "In other words, if I feed it x1a, x2a, and so on, and I add", + "to each corresponding input the b set of inputs, so I get", + "x1b here and x2b here-- so notice that this is here, and", + "the b set of inputs is here.", + "So notice that all I've done is I've added up", + "corresponding inputs.", + "What superposition tells me is that my outputs will be a sum", + "of the corresponding inputs.", + "In other words, if I had ya with the a set of inputs", + "alone, and I had yb with the b set of inputs alone, then if I", + "sum the corresponding inputs, the a and the b inputs, then", + "my output will be a sum of the corresponding outputs as well.", + "And again, jokingly, if I feed apples and blueberries to the", + "input, then in this case, jokingly again, maybe I get", + "mixed fruit jam.", + "How does this yield something interesting for us?", + "Let me do a specific example of the property of", + "superposition and see how this will yield a very interesting", + "technique to analyze linear circuits.", + "Again, remember, both the homogeneity and superposition", + "property applies to linear circuits.", + "So let me take a specific instance of", + "superposition here.", + "And so I take some system, a linear system, and let's say I", + "have two inputs that I apply, v1 and v2.", + "And let's say my goal is to find out what the output is.", + "What I want to show you is that, by the method of", + "superposition, I can use a divide and conquer technique.", + "What I can do is I can take the same system and I can set", + "the v2 output to 0 and apply just the v1.", + "And I measure the corresponding output, y1.", + "So y1 here is the partial output, given that I have", + "applied a v1 alone.", + "Similarly, I take the same system and in this case,", + "second time around, I set v1 to 0, and I apply v2 alone.", + "And then let's say I get y2 as my output", + "with v2 acting alone.", + "Then here is something very interesting.", + "So by superposition from a previous example, recall that", + "if I took one set of inputs and a second set of inputs and", + "I summed up the corresponding values, then superposition", + "said my output would be a sum of the individual outputs with", + "just each of those applied alone.", + "In other words, if I show the v1 as 0 and then if I sum to", + "that the second set of inputs, 0 and v2 from here, so that", + "this got applied here and the first set of inputs got", + "applied here, then what superposition would say is", + "that my output would be a sum of the two partial outputs.", + "In other words, y1 would come from here and y2 would be the", + "same as the y2 with the v2 applied alone.", + "So this is an extremely powerful idea.", + "So to recap, what have I done here?", + "I have used a method of superposition to apply a set", + "of inputs in the following way.", + "I started by saying that I have a circuit and I want to", + "apply v1 and v2 to it and compute the output.", + "Now rather than trying to solve the circuit by applying", + "both v1 and v2, what I did was I broke it up into two", + "sub-problems. In the first sub-problem, what I did was I", + "applied v1 alone and set v2 to 0, and then in the second", + "sub-problem, I applied v2 alone and I set v1 to be 0.", + "And I computed the two partial outputs, y1 and y2.", + "The method of superposition then says that if I took the", + "two corresponding sets of inputs and summed them up,", + "then my output would be a sum of the two partial outputs.", + "Notice that at the input here, if you look at these two", + "inputs, the v1 plus 0 is simply the v1, v2 plus 0 is", + "simply v2, which is the same as what I have here.", + "So in other words, I was able to solve the circuit that", + "contained v1 and v2 as inputs by applying just v1 alone and", + "then v2 alone, and then by summing up the two", + "corresponding outputs.", + "This will yield an incredibly powerful method for us called", + "the method of superposition." + ] +} \ No newline at end of file diff --git a/subs/CdS_Zi6hCeI.srt.sjson b/subs/CdS_Zi6hCeI.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/CdS_Zi6hCeI.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/Duh1RHZGMQ0.srt.sjson b/subs/Duh1RHZGMQ0.srt.sjson new file mode 100644 index 0000000000..d74a1aafbc --- /dev/null +++ b/subs/Duh1RHZGMQ0.srt.sjson @@ -0,0 +1,287 @@ +{ + "start": [ + 140, + 1920, + 4050, + 7780, + 11670, + 13790, + 16775, + 21040, + 22530, + 24520, + 27320, + 30430, + 33450, + 36090, + 37460, + 41160, + 43730, + 48030, + 48790, + 52080, + 55050, + 56430, + 59550, + 63590, + 67390, + 69850, + 73910, + 76660, + 77410, + 80030, + 82200, + 84780, + 88950, + 93500, + 96400, + 98060, + 102300, + 104110, + 107260, + 110820, + 113980, + 118695, + 119250, + 121980, + 126220, + 130270, + 135080, + 138750, + 141600, + 144020, + 147160, + 149750, + 150030, + 153060, + 156260, + 160060, + 162770, + 164880, + 168590, + 168870, + 170560, + 174770, + 177460, + 180290, + 182210, + 183570, + 186930, + 189690, + 193210, + 195810, + 198050, + 202650, + 204340, + 209000, + 211830, + 214500, + 215630, + 220430, + 221500, + 224790, + 227200, + 229290, + 232150, + 235160, + 238490, + 240740, + 245210, + 248470, + 251420, + 252660, + 255480, + 256890, + 260010 + ], + "end": [ + 1920, + 4050, + 7780, + 11670, + 13790, + 16775, + 21040, + 22530, + 24520, + 27320, + 30430, + 33450, + 36090, + 37460, + 41160, + 43730, + 48030, + 48790, + 52080, + 55050, + 56430, + 59550, + 63590, + 67390, + 69850, + 73910, + 76660, + 77410, + 80030, + 82200, + 84780, + 88950, + 93500, + 96400, + 98060, + 102300, + 104110, + 107260, + 110820, + 113980, + 118695, + 119250, + 121980, + 126220, + 130270, + 135080, + 138750, + 141600, + 144020, + 147160, + 149750, + 150030, + 153060, + 156260, + 160060, + 162770, + 164880, + 168590, + 168870, + 170560, + 174770, + 177460, + 180290, + 182210, + 183570, + 186930, + 189690, + 193210, + 195810, + 198050, + 202650, + 204340, + 209000, + 211830, + 214500, + 215630, + 220430, + 221500, + 224790, + 227200, + 229290, + 232150, + 235160, + 238490, + 240740, + 245210, + 248470, + 251420, + 252660, + 255480, + 256890, + 260010, + 261260 + ], + "text": [ + "PROFESSOR: In the previous segment, we looked at the", + "Thevenin method, which applied to linear circuits.", + "And in that method, I could take an arbitrary network, n,", + "containing a whole bunch of sources and resistors where", + "the current sources are voltage sources.", + "And I could replace that with its Thevenin equivalent, where", + "the Thevenin equivalent pattern was given by a voltage", + "source VTH.", + "in series with the resistance RTH.", + "Now one of the things that I want you to think about in", + "circuits is that whenever you have circuits containing", + "voltages and properties involving voltages, you can", + "immediately think of complimentary properties", + "involving current sources.", + "So much as I was able to replace an arbitrary network n", + "with its Thevenin equivalent, you can think about replacing", + "the arbitrary network n with some pattern involving a", + "current source.", + "And indeed, that method where you replace an arbitrary", + "network with a pattern involving a current source is", + "called the Norton method.", + "So in the Norton method, what we do is we are able to", + "replace an arbitrary network n with its Norton equivalent,", + "where the Norton equivalent contains the current source IN", + "in parallel with the resistance RTH.", + "The current source in parallel with RTH is a Norton pattern,", + "and you should contrast it with the corresponding", + "Thevenin pattern.", + "So a voltage source in series with a resistor is a Thevenin", + "pattern, and a current source in parallel with the", + "resistance is the Norton pattern.", + "So in the case of the Norton pattern, which contains the", + "current source IN and the Norton resistance RN, in the", + "same manner that you defined the Thevenin equivalent, we", + "can derive the Norton equivalent.", + "So to obtain the current IN, what you do is you obtain the", + "short circuit current seen at the port.", + "So recall for the Thevenin method, I open-circuited the", + "port here, and measured the voltage, and that was my VTH.", + "So the Norton method, what I do is I short circuit this", + "port and measure the current I. That current is IN, or the", + "Norton current.", + "And then I can get a Norton resistance RN--", + "oh, I should say RN here-- the Norton resistance RN, which,", + "incidentally, is identical to the Thevenin resistance RTH.", + "I can get that in the same manner as I got RTH, which is", + "I shut off all the independent voltage sources and current", + "sources and simply take the resistance measure at the", + "port, of course, without the short.", + "I go ahead and measure the resistance seen at the port", + "with all the voltages and currents turned off.", + "OK?", + "That would be my Norton resistance, RN.", + "So again, we stated this pattern, a current source IN", + "parallel to a Norton resistance RN, where this", + "corresponds to the Thevenin equivalent, where I have VTH", + "and RTH in series.", + "So the Norton is the dual of the Thevenin.", + "OK?", + "Where the Thevenin is the voltage in series with the", + "resistance, and its dual is the Norton equivalent, which", + "is the current source in parallel with resistance.", + "An immediate question that comes to mind is how are the", + "Thevenin and Norton equivalents", + "related to each other?", + "After all, they are the duals of one another.", + "And so notice the Thevenin equivalent on the left-hand", + "side and the Norton equivalent on the right-hand side.", + "The resistances RTH and the Norton", + "resistance RN are equal.", + "And then we can also relate the Norton current IN and the", + "Thevenin voltage as follows.", + "IN is VTH divided by RTH.", + "And so if you take the Thevenin voltage and divide", + "that by the Thevenin resistance, you get the Norton", + "current, IN.", + "So this very quickly shows you how you can go from the Norton", + "to the Thevenin.", + "One question I am often asked is when do I use the Thevenin", + "method and when do I use the Norton method?", + "Well, you know, that comes from experience.", + "Like you look at circuits in one of our earlier examples", + "where the external network contained a voltage source in", + "series with a resistance, it made sense to take the rest of", + "the network and turn that into Thevenin equivalent.", + "However, if I have a basic circuit containing a current", + "source and a resistance in parallel, then it might be", + "easier to take my external network and convert that into", + "a Norton equivalent.", + "So, really, when you want to get things in", + "parallel, think Norton.", + "When you want to get things in series to simplify analysis,", + "think Thevenin." + ] +} \ No newline at end of file diff --git a/subs/EWD-sNLs2Xw.srt.sjson b/subs/EWD-sNLs2Xw.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/EWD-sNLs2Xw.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/FGx1I9LAIGs.srt.sjson b/subs/FGx1I9LAIGs.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/FGx1I9LAIGs.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/IzULGSWdcGk.srt.sjson b/subs/IzULGSWdcGk.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/IzULGSWdcGk.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/KawScqSYew0.srt.sjson b/subs/KawScqSYew0.srt.sjson new file mode 100644 index 0000000000..fe8b0e2a73 --- /dev/null +++ b/subs/KawScqSYew0.srt.sjson @@ -0,0 +1,515 @@ +{ + "start": [ + 0, + 3390, + 6630, + 8860, + 10230, + 12240, + 13650, + 17510, + 20900, + 23500, + 26410, + 29420, + 32790, + 34430, + 37960, + 40480, + 43120, + 45440, + 47790, + 50481, + 54750, + 55970, + 59050, + 61500, + 66830, + 68220, + 72570, + 75820, + 77090, + 80440, + 81730, + 82690, + 86640, + 88250, + 91710, + 94460, + 98490, + 101010, + 104440, + 106330, + 110200, + 112150, + 114880, + 115950, + 120080, + 123360, + 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450400, + 456240, + 459490, + 462760, + 467780, + 469050, + 473020, + 476450, + 478540, + 480890, + 483820, + 488470, + 490360, + 494010, + 498550, + 502320, + 503210, + 507460, + 511190, + 514760, + 518520, + 520780, + 524169 + ], + "end": [ + 3390, + 6630, + 8860, + 10230, + 12240, + 13650, + 17510, + 20900, + 23500, + 26410, + 29420, + 32790, + 34430, + 37960, + 40480, + 43120, + 45440, + 47790, + 50481, + 54750, + 55970, + 59050, + 61500, + 66830, + 68220, + 72570, + 75820, + 77090, + 80440, + 81730, + 82690, + 86640, + 88250, + 91710, + 94460, + 98490, + 101010, + 104440, + 106330, + 110200, + 112150, + 114880, + 115950, + 120080, + 123360, + 129470, + 130880, + 134280, + 137320, + 141740, + 143440, + 147540, + 149270, + 150720, + 155540, + 158830, + 160350, + 165280, + 168060, + 172520, + 175240, + 178160, + 180840, + 186180, + 187580, + 191830, + 194560, + 195960, + 201270, + 205060, + 209160, + 210440, + 213540, + 214880, + 217650, + 220690, + 224440, + 228110, + 229210, + 233620, + 235660, + 240930, + 242870, + 247360, + 251630, + 255320, + 258470, + 260459, + 262440, + 268210, + 270080, + 272000, + 276520, + 280750, + 287050, + 294450, + 297010, + 298840, + 304120, + 307810, + 311080, + 315010, + 316780, + 320540, + 321340, + 325690, + 330430, + 333260, + 337390, + 338710, + 341890, + 344160, + 346660, + 350840, + 352590, + 356250, + 358370, + 361140, + 364930, + 368810, + 372380, + 377050, + 378390, + 381330, + 382290, + 384000, + 387350, + 390380, + 394590, + 396850, + 398200, + 401730, + 406830, + 409150, + 412350, + 416120, + 423780, + 424960, + 429970, + 431510, + 434490, + 436480, + 437950, + 441870, + 445970, + 450400, + 456240, + 459490, + 462760, + 467780, + 469050, + 473020, + 476450, + 478540, + 480890, + 483820, + 488470, + 490360, + 494010, + 498550, + 502320, + 503210, + 507460, + 511190, + 514760, + 518520, + 520780, + 524169, + 528000 + ], + "text": [ + "PROFESSOR: So far in 6.002, you've seen how by making some", + "simplifications of Maxwell's equations, we've ended up with", + "very simple algebraic laws that can be", + "used to analyze circuits.", + "And in this little playground of ours,", + "really good things happen.", + "This is our EECS playground, where by making some", + "simplifications, we've been able to really come up with", + "very simple techniques for analyzing circuits.", + "So today, as we build up our arsenal of techniques for", + "analyzing circuits, we'll look at a further simplification.", + "We're going to look at a part of this playground in which", + "linear circuits reside.", + "These kinds of circuits allow us to use some even more", + "powerful techniques to analyze them.", + "These new techniques that you will learn today include", + "superposition, Thevenin and Norton.", + "It's pretty amazing to think of these techniques as the", + "bazookas of EECS.", + "OK, let me start with a quick review as is my usual practice", + "of what we've seen so far.", + "So the circuit analysis method you've seen so far include,", + "first of all, the KVL, KCL method.", + "In this method, the KVL, KCL, and the element rules are used", + "to analyze circuits.", + "The KVL method, as you've seen before, is one where you take", + "the various voltages in a loop in a circuit and they should", + "all sum to zero.", + "Similarly, the currents at any given node,", + "must also sum to zero.", + "That's KCL.", + "And so you apply these KVL, KCL and element rules to", + "circuits, and then go solve them.", + "But we did see that they ended up with a very large number of", + "equations that were quite messy to resolve.", + "The second technique that we looked at last week included", + "circuit decomposition rules, where you applied some of", + "these rules to compose resistors and other elements,", + "and solved circuits that way.", + "And then, we looked at the node method, where you chose a", + "ground in a circuit.", + "And then you applied KCL at each of the nodes, the", + "reference to the ground node.", + "And what was interesting is that the KVL was implicit in", + "the pattern that you used in the node method, where the", + "pattern was the ei minus ej, divided by the resistance of a", + "given [UNINTELLIGIBLE].", + "And this was a pattern that you really borrowed from KVL,", + "and this was implicitly used in the node method.", + "The node method, of course, is the workhorse of 6.002 and can", + "be applied to all kinds of circuits.", + "It really applies in the entire playground of ours.", + "So when in doubt, simply go ahead and", + "apply the node method.", + "OK, as I promised, we'll now look at the smaller region of", + "the playground, and see if some interesting things happen", + "in that playground.", + "So to give you a quick review, let me start by looking at", + "some basic properties of linear circuits.", + "Following that, I will look at the superposition tool kit for", + "your arsenal of techniques to analyze circuits.", + "And then I will talk about the Thevenin method.", + "And finally, I'll talk about the Norton method.", + "OK, so let's get started with linear circuits and see what", + "linearity means.", + "So I want to do an example using the following little", + "circuit, in which I have a voltage source", + "and a current source.", + "And my goal here is to find the voltage at this node e.", + "And I'm going to pick a ground node here and find the voltage", + "e referenced to this ground node that I've just", + "marked out for you.", + "So to analyze a circuit, you're supposed to write down", + "the node equations.", + "And write down the mode equations for the node.", + "That's the only node for which we have an unknown.", + "Recall that I have another node here, but because that is", + "connected by a voltage source to ground, its voltage is", + "simply V.", + "OK, let's start by writing the node equations for the node", + "with unknown voltage e.", + "So let's start by looking at the current that goes from the", + "node with voltage e to the left.", + "And so I take e minus V divided by R1.", + "That is the current headed in the direction from e to v.", + "And then I add the current that is going down this edge.", + "That is just simply e divided by R2.", + "And then I take the current that is", + "headed in this direction.", + "And that is simply minus I. According to the KCL rule,", + "they all sum up to 0.", + "So the first thing you will notice as you write the node", + "equation right away is that this equation here shows you", + "that it is linear in the various voltages and currents", + "e, V, and I. In other words, you don't have terms, no terms", + "that are eV, or V squared, or VI, and so on.", + "So this circuit here is", + "characterized by the node equation.", + "And notice that it is linear in the e, V, and I terms.", + "OK, let's go ahead and look at this in some more detail.", + "And I'm going to simplify the equation a little bit more to", + "really get a much clearer sense of the linearity here.", + "So I've written down the node equation.", + "And I'm going to simplify by rearranging some of the terms", + "in the equation.", + "So let me collect the various coefficients.", + "So let me write down e on this side, and look at and collect", + "all the terms that multiply e.", + "So I see a 1 by R1 term here.", + "Let me write that down.", + "I see a 1 by R2 term.", + "And so e is my unknown.", + "Let we collect the knowns on the right-hand side.", + "So one of the knowns is I. So let me move it to the", + "right-hand side and put that there.", + "The other known is this one here, V divided by R1.", + "I'm going to take it to the right-hand side.", + "It becomes plus V divided by R1.", + "So let me introduce a little bit of nomenclature here.", + "So notice I've rearranged the terms. And I get some", + "coefficients multiplying e, and that is a sum of the", + "sources, V and I, where V has been scaled by", + "1 divided by R1.", + "So when you look at these terms, let's understand a", + "couple of things.", + "Let's understand a couple of things right away.", + "So if you look at the coefficient of the unknown e,", + "in general when you have a much larger circuit, it is not", + "a single value, but rather it is a matrix of values.", + "And it's just good to know these terms. It's called a", + "conductance matrix.", + "Similarly, it's usually given the symbol G.", + "Similarly, the node voltages becomes a column vector of", + "node voltages, and it's given the label e.", + "And then, on the right-hand side, you have the linear sum", + "of sources, and that is given the term S. And so you get the", + "form G times e equals S, where G is a matrix usually, e is a", + "column vector.", + "And similarly, the sum of sources ends up being a column", + "vector as well.", + "So with that bit of cultural background in terms of what", + "these things are called in general, let me", + "simplify them further.", + "And what I get now is--", + "let's try to have e on the left-hand side all by itself,", + "and divide both sides by the coefficient of e.", + "And this guy here, if I simplify it, becomes R1 R2", + "divided by R2 plus R1.", + "So when I multiply out both sides by that, what I end up", + "getting is I have a V here, and I have the I here.", + "So what is the coefficient of V?", + "So I multiply both sides by R1 R2.", + "And so R1 and R1 cancel out.", + "So I end up with R2 at the top.", + "And I get R1 plus R2 down here.", + "Similarly, so what do you think we get for I here?", + "For I, I end up with R1 R2 divided by R1", + "plus R2 down here.", + "So notice that the linearity becomes much more obvious at", + "this point where my unknown e is some constant coefficient", + "times the voltage v and some constant coefficient times the", + "current I.", + "In other words, e is of the following form. e is some", + "constant coefficient times my first source, some constant", + "coefficient times V2, and so on.", + "Plus some other coefficient times I1, some other", + "coefficient times I2, and so on.", + "So if you look at this form here, notice that this is", + "linear in the sources VIs and IIs." + ] +} \ No newline at end of file diff --git a/subs/Q3IF4g9eH34.srt.sjson b/subs/Q3IF4g9eH34.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/Q3IF4g9eH34.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/T2NRdHHQlOA.srt.sjson b/subs/T2NRdHHQlOA.srt.sjson new file mode 100644 index 0000000000..442bd545f2 --- /dev/null +++ b/subs/T2NRdHHQlOA.srt.sjson @@ -0,0 +1,167 @@ +{ + "start": [ + 160, + 6070, + 11030, + 12260, + 15910, + 20200, + 21230, + 25235, + 28170, + 32990, + 36420, + 39500, + 43190, + 48010, + 53840, + 56590, + 60500, + 64310, + 68250, + 70030, + 73220, + 77210, + 80920, + 84820, + 86620, + 89910, + 93140, + 97560, + 99070, + 102100, + 104730, + 109310, + 110310, + 115590, + 117910, + 121150, + 124740, + 127830, + 130419, + 135490, + 140610, + 144660, + 149890, + 153040, + 155790, + 160590, + 162220, + 169490, + 174110, + 178340, + 183420, + 188440, + 191370 + ], + "end": [ + 6070, + 11030, + 12260, + 15910, + 20200, + 21230, + 25235, + 28170, + 32990, + 36420, + 39500, + 43190, + 48010, + 53840, + 56590, + 60500, + 64310, + 68250, + 70030, + 73220, + 77210, + 80920, + 84820, + 86620, + 89910, + 93140, + 97560, + 99070, + 102100, + 104730, + 109310, + 110310, + 115590, + 117910, + 121150, + 124740, + 127830, + 130419, + 135490, + 140610, + 144660, + 149890, + 153040, + 155790, + 160590, + 162220, + 169490, + 174110, + 178340, + 183420, + 188440, + 191370, + 193410 + ], + "text": [ + "PROFESSOR: OK, so i1 is very quickly calculated by taking", + "the difference of V and VTH and dividing that by the sum", + "of the two resistances.", + "So the current i1, flowing in this direction, is given by V", + "minus VTH divided by R1 plus RTH.", + "And there I have it.", + "Notice that by converting the arbitrary network N into the", + "Thevenin equivalent, I turn this into a really trivial", + "problem where I could write down i1 simply by inspection.", + "Finally, before we move off the topic of the Thevenin", + "network and the Thevenin method, it is worthwhile", + "staring at this pattern here comprising the voltage source", + "in series with the resistance and the equation v equals vTH", + "plus RTHi that governs the vi of the Thevenin pattern.", + "So it's worthwhile looking at this graphically as well.", + "So I'm going to show you a little graph here and plot the", + "iv relation for this Thevenin pattern.", + "And usually the way you draw these iv relations is you try", + "to find out an open-circuit voltage.", + "In other words, try to find out of the voltage when the", + "current is 0, so open-circuit voltage when i is 0.", + "So in this case, when i is set to 0 and there's no current,", + "then the open-circuit voltage here is simply", + "vTH so v equals vTH.", + "So in other words, when the current is 0,", + "my voltage is vTH.", + "So I found one point on the iv relation for the Thevenin", + "equivalent pattern.", + "Next, let me find out the short-circuit current.", + "And for the short circuit, v is set to 0.", + "So in this case, I apply a short circuit here, and I'm", + "going to measure the current.", + "So the current in this case, i is given by minus", + "vTH divided by RTH.", + "Notice that because vTH is positive here, the current", + "flows down in this direction and is given by vTH divided by", + "RTH, and that is in a direction opposite to i.", + "And so therefore, I get the minus sign.", + "So my current is given by minus vTH divided by RTH.", + "And so for 0 volts, I get some current here, and that is", + "given by vTH divided by RTH.", + "And so this voltage here is my open-circuit voltage, and this", + "current here is my short-circuit current, OK?", + "So this is my short-circuit current, and that's my", + "open-circuit voltage, and my iv relation is drawn by simply", + "connecting the two points.", + "And the slope of this curve is given by 1 divided by RTH.", + "So here again, to very quickly summarize, I've drawn the iv", + "relation for this definite pattern, which has a vTH in", + "series with an RTH and found two points on the iv relation.", + "One is on the voltage axis, and one is on the current axis", + "by measuring the open-circuit voltage and the short-circuit", + "current, and then drawing a line through them." + ] +} \ No newline at end of file diff --git a/subs/TwQScW8yLek.srt.sjson 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newline at end of file diff --git a/subs/i9zDhWrNK5M.srt.sjson b/subs/i9zDhWrNK5M.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/i9zDhWrNK5M.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/jDyHfyAssLA.srt.sjson b/subs/jDyHfyAssLA.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/jDyHfyAssLA.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/kZj5cQ4SQrE.srt.sjson b/subs/kZj5cQ4SQrE.srt.sjson new file mode 100644 index 0000000000..7e36e20308 --- /dev/null +++ b/subs/kZj5cQ4SQrE.srt.sjson @@ -0,0 +1,326 @@ +{ + "start": [ + 370, + 3130, + 5940, + 10140, + 11110, + 14040, + 18460, + 22350, + 23090, + 26720, + 30230, + 32880, + 35550, + 38650, + 39220, + 41830, + 45920, + 48890, + 51430, + 52850, + 55930, + 59070, + 62330, + 63930, + 67940, + 69860, + 72030, + 73080, + 75110, + 77490, + 80530, + 83770, + 85680, + 89460, + 91120, + 94850, + 95980, + 98780, + 101630, + 104630, + 106790, + 107870, + 111670, + 116240, + 118560, + 122970, + 125130, + 127540, + 128720, + 132380, + 133390, + 135970, + 138150, + 142360, + 146730, + 149530, + 151130, + 152620, + 155110, + 158190, + 160750, + 163740, + 165210, + 168750, + 172200, + 174980, + 176780, + 178720, + 181080, + 182020, + 183930, + 187000, + 189920, + 193320, + 195830, + 200040, + 203050, + 203870, + 205650, + 208250, + 210600, + 211935, + 213550, + 215960, + 217135, + 219680, + 222100, + 225380, + 226060, + 229100, + 229750, + 232600, + 235800, + 238050, + 240410, + 242740, + 244240, + 246230, + 249050, + 252620, + 255720, + 259300, + 262120, + 264750, + 266140, + 269450 + ], + "end": [ + 3130, + 5940, + 10140, + 11110, + 14040, + 18460, + 22350, + 23090, + 26720, + 30230, + 32880, + 35550, + 38650, + 39220, + 41830, + 45920, + 48890, + 51430, + 52850, + 55930, + 59070, + 62330, + 63930, + 67940, + 69860, + 72030, + 73080, + 75110, + 77490, + 80530, + 83770, + 85680, + 89460, + 91120, + 94850, + 95980, + 98780, + 101630, + 104630, + 106790, + 107870, + 111670, + 116240, + 118560, + 122970, + 125130, + 127540, + 128720, + 132380, + 133390, + 135970, + 138150, + 142360, + 146730, + 149530, + 151130, + 152620, + 155110, + 158190, + 160750, + 163740, + 165210, + 168750, + 172200, + 174980, + 176780, + 178720, + 181080, + 182020, + 183930, + 187000, + 189920, + 193320, + 195830, + 200040, + 203050, + 203870, + 205650, + 208250, + 210600, + 211935, + 213550, + 215960, + 217135, + 219680, + 222100, + 225380, + 226060, + 229100, + 229750, + 232600, + 235800, + 238050, + 240410, + 242740, + 244240, + 246230, + 249050, + 252620, + 255720, + 259300, + 262120, + 264750, + 266140, + 269450, + 270700 + ], + "text": [ + "SPEAKER 1: At this point, I'd like to do a quick summary of", + "all that we have covered in 6.002 so far.", + "We began life in 6.002 by discretizing matter into", + "lumped elements.", + "And we agreed to observe the lumped matter discipline.", + "What this did was it turned real life elements, as our", + "little pickle on which we performed the fun experiment a", + "little while ago.", + "And we were able to turn that into lumped elements, such as", + "a resistor, which we could use in circuits to obtain", + "properties such as voltages and currents.", + "And when we took these lumped elements and put them together", + "into circuits, we got the lumped circuit abstraction.", + "All right.", + "So once we built these circuits containing these", + "lumped elements, we then went on to develop an arsenal of", + "tools that we could use to analyze circuits.", + "So notice that the fun part of 6.002 doubled", + "has really not begun.", + "We just made some assumptions that allowed us to make the", + "transition from physics and the complications of Maxwell's", + "equations into some very simple territories where", + "algebraic equations rule.", + "And then, we sat down and developed some analysis", + "techniques for the circuits that we built.", + "Notice we really haven't built anything useful or", + "done any fun stuff.", + "We are still developing our tools for the", + "circuits that we created.", + "So we developed a bunch of circuit analysis methods.", + "We started off with the KVL, KCL method.", + "And in this method, you took a circuit.", + "And you wrote the KVL, KCL equations and also the I-V", + "relations for each of the elements.", + "And then you got a whole series of linear equations.", + "And we went and solved them.", + "The second technique we learned was applying", + "simplification rules, where you combine resistances in", + "series and so on and so forth, a resistance in parallel or a", + "voltage in series, and then used those to", + "simplify the circuit.", + "The third method that we developed was the node method.", + "The node method is really the workhorse of our industry.", + "When in doubt, use the node method.", + "The node method applies to all circuits and, in fact, is used", + "for linear or nonlinear circuits.", + "And by and large, when in doubt, we just", + "apply the node method.", + "So if you look at these techniques here, they apply to", + "any network.", + "And then, we looked at another class of techniques, the", + "superposition, Thevenin, and Norton.", + "In the superposition method, we simplified a circuit into", + "subcircuits by shutting off all sources save for one.", + "And then we found the subcircuit result.", + "And then we added up all the results.", + "That was the superposition method.", + "And then we learned about the Thevenin and Norton methods.", + "The Thevenin method, it determined a Thevenin pattern", + "circuit to replace an arbitrary network, while the", + "Norton method replaced an arbitrary circuit with the", + "Norton pattern.", + "Now, don't forget that the superposition, Thevenin, and", + "Norton methods apply only to linear circuits.", + "So these techniques, superposition, Thevenin and", + "Norton, are extremely powerful.", + "And they will work with linear networks.", + "And we will see a lot of situations where we have", + "linear networks.", + "And so these are very important techniques.", + "And then, of course, for nonlinear networks, or for", + "networks that contain nonlinear elements, we will", + "largely use the node method, where the node method is", + "really the workhorse of our industry.", + "Now people often ask me, when do I use which technique?", + "You've taught us the KVL, KCL method, the node method, the", + "Norton method.", + "Where do I apply these techniques?", + "The way to think about it is just imagine if you are a", + "carpenter, and you have a tool chest full of tools.", + "You know, you have a chisel.", + "You have a screwdriver.", + "And you have my favorite tool, a chainsaw.", + "So you have all of these tools.", + "And if you asked a carpenter, well, where do you use which", + "tool, what do you expect the carpenter would respond?", + "The carpenter would say, well, that's why you pay a carpenter", + "the big bucks.", + "They know what tool to use where, and they're practiced", + "in using it.", + "Similarly, as engineers, as you get more practice, you", + "will begin using these tools and beginning to figure out", + "where to use what tool.", + "But fundamentally, the superposition, Thevenin, and", + "Norton methods apply to linear networks.", + "And the node method applies anywhere.", + "So when in doubt, just use the node method.", + "And much like a carpenter would use a chainsaw to chop", + "down a tree, you can use your superposition method to", + "analyze circuits that contain a number of sources, where you", + "can break it down into very simple subcircuits.", + "But of course, the circuit has to be linear to begin with.", + "So really, you will develop experience in terms of where", + "to apply which method.", + "But again, don't forget that the node method will apply in", + "any situation." + ] +} \ No newline at end of file diff --git a/subs/uvDLK-DV0qw.srt.sjson b/subs/uvDLK-DV0qw.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/uvDLK-DV0qw.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/wBk29tcxFDc.srt.sjson b/subs/wBk29tcxFDc.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/wBk29tcxFDc.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/wfVUho4Nr3c.srt.sjson b/subs/wfVUho4Nr3c.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/wfVUho4Nr3c.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/xal6k2pwvgA.srt.sjson b/subs/xal6k2pwvgA.srt.sjson new file mode 100644 index 0000000000..d96b61df2d --- /dev/null +++ b/subs/xal6k2pwvgA.srt.sjson @@ -0,0 +1,635 @@ +{ + "start": [ + 270, + 3520, + 5500, + 8910, + 11210, + 14260, + 17840, + 21030, + 23940, + 26650, + 29010, + 32360, + 34280, + 37110, + 39430, + 43440, + 47610, + 52260, + 56170, + 59750, + 61630, + 64500, + 65480, + 69130, + 73940, + 77900, + 79720, + 81090, + 84250, + 86890, + 89910, + 93520, + 96940, + 99170, + 101660, + 105100, + 111580, + 114550, + 117470, + 121980, + 126090, + 130560, + 135780, + 139920, + 143700, + 146090, + 148460, + 149910, + 152710, + 155260, + 160280, + 162080, + 165570, + 168340, + 171250, + 174230, + 176280, + 180140, + 182290, + 186800, + 190170, + 194470, + 197510, + 200390, + 204380, + 208040, + 211100, + 215350, + 217510, + 221940, + 225380, + 228770, + 232580, + 234870, + 237940, + 242040, + 246600, + 249500, + 250720, + 254400, + 259290, + 260190, + 263610, + 264910, + 268250, + 269630, + 274030, + 277480, + 280870, + 281700, + 284180, + 285580, + 292210, + 295220, + 296380, + 300620, + 304190, + 305380, + 309370, + 313070, + 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624350, + 625830, + 628770, + 630350, + 635770, + 641350, + 643040, + 646225, + 650990, + 654300, + 657140, + 659880, + 664240, + 668170, + 670810, + 672060 + ], + "text": [ + "PROFESSOR: In this segment, we will develop a second method", + "that will work for linear circuits.", + "This method is called the Thevenin method, and its", + "complementary method, the Norton method.", + "So in order to develop this method for linear circuits,", + "suppose you have some arbitrary network, N. And", + "let's say in this arbitrary network you have a whole bunch", + "of resistors, you have a whole bunch of voltage sources, Vm,", + "and a whole bunch of current sources as well.", + "OK, so you have a bunch of voltage sources.", + "And these are all independent voltage sources for now.", + "V1, V2, V3, all the way through VM.", + "You have a whole bunch of current sources, I1, I2, I3,", + "all the way through to In.", + "Suppose I am interested in applying some kind of", + "excitation due to an external current source with current i.", + "And let us say that all I care to do is to determine the", + "voltage, V. So the setup here is I have an arbitrary", + "network, N, with a ton of resistors and voltage sources", + "and current sources, all independent.", + "And I apply an external excitation, and", + "it's a current i.", + "And just assume that all I want to do is to determine the", + "voltage, V. Assume that I don't care about any internal", + "voltages, Vi, or any internal currents, Ij, and so on.", + "Let's say I don't care about any of", + "those internal currents.", + "All I care about is the voltage, V.", + "So in a situation like this where you care about some", + "voltage or current at some point, you can use the", + "property of linearity and the resulting superposition", + "property to develop an extremely powerful method to", + "get you to your answer very quickly.", + "So in order to develop this method, let me use the", + "superposition technique and try to figure out the voltage,", + "V. So the voltage V will be some combination of the linear", + "sources in this linear circuit.", + "So let's say, for example, I want to figure out the", + "contribution to the voltage V due to the voltage source, Vm.", + "What I would then do is I would set i to 0, I would set", + "all the currents, I1 through In, to 0, and I would set all", + "the voltages, V1 through Vm minus 1, to 0 as well, and", + "just look at the impact on V due to Vm acting alone.", + "So the impact on V due to Vm acting alone, and notice that", + "once all the currents have been turned off and all the", + "other voltages have been turned off, I'm left with a", + "big resistor network.", + "And I'm going to get some multiplier here.", + "Let's label that alpha m.", + "So that will be the result of the source Vm acting alone on", + "the output voltage, V.", + "Similarly, I can do the same thing for all the voltages.", + "I can do it for V1 acting alone.", + "I can do it for V2 acting alone, and so on and so forth.", + "For each of those voltages, V1, V2, and so on, I get a", + "term that looks like this.", + "I get alpha 1 V1, alpha 2 V2, and so on and so forth, all", + "the way through alpha m Vm.", + "And so what I get is a sum over m of all of these terms.", + "By applying V1 acting alone and V2 acting alone and so on,", + "I get a term, alpha 1 V1, alpha 2 V2, and so on.", + "Next, I'll move on to the currents, and in this case,", + "supposing I set all the currents, say, for In--", + "I'm going to set the small i to 0, and I'm going to set all", + "the Vm's to 0, and I'm going to set all the currents, I1", + "through In minus 1, to 0.", + "So in that situation, I'm going to get some factor, Bn,", + "that applies to In.", + "So I've got some factor Bn, beta n, that applies to In.", + "And that is the result of In acting alone.", + "Similarly, I can have I1 acting alone, I2 acting alone,", + "and so on, and for each of them, I get a term, beta 1 I1", + "plus beta 2 I2 and so on and so forth.", + "And I sum them all up as well over all n.", + "So with i acting alone, I'm going to set all of the other", + "In's and Vm's to 0, and just have i acting alone.", + "And so therefore I will get an i, and I'm going to have some", + "multiplier.", + "And in this case, notice that when all the Vm's and all the", + "In's are set to 0, I'm just left with a big resistor", + "network here.", + "And so it will look like a big effective resistor looking", + "into this port.", + "And so let me write that down as some R multiplied", + "by the current i.", + "So notice now that the voltage V is a sum of a bunch of", + "components that arise from the voltages acting alone, the", + "currents acting alone, and also the external excitation", + "acting alone.", + "And just recall, how did I get this?", + "How did I get each of these terms?", + "So this term which sums up all the voltages I got by setting", + "all the In's to 0 and by setting the external", + "excitation to 0.", + "Similarly, I got the second term here by setting all the", + "voltage sources to 0, and also by setting the external", + "excitation to 0.", + "And finally, this last term, I got that by setting all the", + "currents to 0 and all the voltages to 0.", + "So what we're going to do now is by using this insight,", + "we're going to build up a new technique.", + "And to give you a preview to that technique, I'm going to", + "show you a trick that will enable you to replace this", + "network, N, by something very, very simple.", + "In fact, I'm going to show you that we're going to be able to", + "replace that entire network by some voltage source and some", + "resistor acting in series.", + "And this will be able to replace this entire network,", + "N, for the purpose of computing the voltage, V. So", + "just think of that as a preview of upcoming", + "attractions.", + "So moving on, let's take a look at the equation that we", + "just developed and understand that a little bit more.", + "So if you look at the equation here that we developed, V is", + "some component related to Vm's, some component related", + "to In's, and some component related to the external", + "excitation, i.", + "So if you look at this term here, if you look at the alpha", + "m term here, that has no units.", + "It has no units because I have a voltage on the left-hand", + "side and it's multiplying a voltage.", + "Similarly, beta and In must result in a voltage, and so", + "therefore beta n must have resistance units.", + "And then similarly, R that is multiplying i must have", + "resistance units as well.", + "So notice that if you look at the Vm-related term and the", + "In-related term, then what you see is that together they are", + "independent of the external excitation, and the behave", + "like a voltage.", + "Similarly, if you look at the right-hand term here, Ri,", + "that's a resistance multiplied by a current, and of course,", + "that also has resulting voltage units.", + "So let's look at the first part here, the part comprising", + "the Vm's and the In's.", + "That behaves like a voltage, and it is independent of", + "external excitation.", + "And so what I'm going to do is I am going to call it VTH.", + "And don't worry about why I'm calling it VTH right now, but", + "let's assume that I call it VTH.", + "So that's a first component that is independent of", + "external excitation and behaves like a voltage.", + "Now if you look at the second component, as I said earlier,", + "the second component clearly depends on the current, i.", + "But if you look at the multiplier R, then that is", + "also independent of external excitation and", + "behaves like a resistor.", + "So let's call that RTH.", + "So again, if you look at the term that gives you V, it will", + "now comprise a portion that we've called VTH.", + "And it has a second component that relates to the external", + "excitation, i, by is multiplied by something we", + "call RTH, where the RTH is independent of the external", + "excitation, i.", + "So what I've just done is I've written down the excitation as", + "a sum of a voltage here that I decided to call VTH, and I've", + "also said that the second part is RTH times i.", + "And that is equal to the voltage, V. So notice V equals", + "VTH plus RTH i.", + "So in other words, if you look at this expression here, as", + "far as the external world is concerned-- and again, for the", + "purpose of computing the voltage, our network N is", + "completely indistinguishable from another network.", + "What does that network look like?", + "So this whole network, N, can be replaced by the following", + "network that I'm going to show you in a quick second.", + "So I have a voltage, VTH, here, and I have", + "a resistance, RTH.", + "And this is my voltage, V. And what I've done here is,", + "according to this equation, V equals VTH plus RTH i--", + "I have simply expressed that in circuit form as a little", + "pattern showing a VTH and then with an RTH in series.", + "And this is easy to see, that when i is 0, the voltage at", + "the output here is VTH.", + "And then if I have a short circuit where V is 0, then the", + "current through that short circuit will simply be given", + "by VTH divided by RTH.", + "And so this little pattern here can now replace my", + "network N for the purpose of computing V.", + "This network is called the Thevenin equivalent network.", + "And so I can take this network, replace the arbitrary", + "network N with this network, the Thevenin equivalent", + "network, and then I can connect my external", + "excitation, i, and then compute the voltage V that", + "appears across the terminals.", + "In other words, what I've done is, using the Thevenin method,", + "I can take an arbitrary network N. I can figure out", + "the VTH and RTH that relate solely to that network's", + "properties, and then replace that network with", + "VTH and RTH in series.", + "And the series connection is called the", + "Thevenin equivalent network.", + "So you will see this is another pattern.", + "This is called the Thevenin pattern.", + "So in circuits and electronics courses, you will see the", + "Thevenin pattern very often.", + "And in this pattern, you have a voltage source in series", + "with a resistor.", + "And again, it's easy to see that when you have I being 0,", + "then the Thevenin voltage, VTH, appears at the output", + "terminal as a VTH.", + "And similarly, if you short the terminal pair here where V", + "is 0, then your current is going to be given by the", + "expression, VTH divided by RTH.", + "And since the current is going to be in the direction", + "opposite to this current, i, there will be a negative.", + "But essentially you can see why this expression, V equals", + "VTH plus RTH i, directly relates to the Thevenin", + "pattern with the voltage source in series with the", + "resistance." + ] +} \ No newline at end of file diff --git a/subs/y07TZVIQIw4.srt.sjson b/subs/y07TZVIQIw4.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/y07TZVIQIw4.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/z4Bw9Vvx7es.srt.sjson b/subs/z4Bw9Vvx7es.srt.sjson new file mode 100644 index 0000000000..243a726425 --- /dev/null +++ b/subs/z4Bw9Vvx7es.srt.sjson @@ -0,0 +1,569 @@ +{ + "start": [ + 120, + 2540, + 3310, + 6590, + 7500, + 11040, + 16100, + 18490, + 19390, + 24450, + 28923, + 29910, + 33840, + 36510, + 38810, + 42210, + 46060, + 50180, + 52280, + 54600, + 58820, + 62380, + 64290, + 66460, + 69690, + 73330, + 77340, + 78390, + 80960, + 83950, + 86870, + 89980, + 93140, + 95340, + 96780, + 99670, + 102155, + 103640, + 105280, + 109240, + 112850, + 114820, + 118260, + 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And VTH here in the Thevenin network", + "is simply the open circuit voltage seen at", + "the terminal pair.", + "In other words, if I looked at network N and I simply", + "measured the voltage at the terminal pair, it has to be an", + "open circuit voltage.", + "That is, without anything connected there, then whatever", + "voltage I measure there would be the Thevenin voltage.", + "Notice that you can see the same thing here.", + "If I measure the voltage at that point, without any", + "external excitation, with an open circuit here, then VTH", + "would directly appear at the terminal, and I would be able", + "to measure the Thevenin voltage.", + "Similarly, what is RTH ?", + "RTH is simply the resistance of the network seen at the", + "terminal there, with all the voltages, Vm's, and all the", + "currents, In's, set to 0.", + "In other words, the way you can find the Thevenin", + "resistance of a network is simply set all the voltages", + "engines and all the currents to 0, and then go ahead and", + "simply measure the resistance looking into", + "that terminal pair.", + "And that will give you RTH.", + "Again, as a quick summary, given any network n, and this", + "case a network with independent voltage and", + "current sources, I can find a Thevenin equivalent which", + "comprises a Thevenin voltage, VTH, and a", + "resistance, RTH, as follows.", + "I open-circuit the connection.", + "In other words, I don't connect anything to the", + "terminal pair when I'm measuring the voltage V. I", + "measure the open circuit voltage there,", + "and that is my VTH.", + "Then I turn off all my current sources and voltage sources", + "inside the network N, and simply measure its resistance.", + "And that is RTH.", + "So that's how I can get RTH and VTH by measurement.", + "And for the purpose of computing some property such", + "as the voltage when an external excitation is", + "applied, I can use those values of VTH and RTH to", + "replace the entire arbitrary network N with this Thevenin", + "equivalent pattern.", + "This is a very, very powerful technique, and we will see", + "some examples of this shortly.", + "OK.", + "So we are ready to define the Thevenin method.", + "So in the Thevenin method, you are given some network N,", + "maybe a horrendous network with a whole bunch of voltage", + "sources and current sources and resistors and", + "so on and so forth.", + "And you have some other external", + "network, E. E for external.", + "Then what I can do is, by the Thevenin method, I can break", + "this down into a simpler problem as follows.", + "What I would do as a first step is I would replace the", + "network N with this Thevenin equivalent.", + "And then as my second step, I would solve with the external", + "network, E.", + "So in other words, what I would do is I would replace", + "the network N with its Thevenin equivalent as my", + "first step.", + "And then I would go ahead and solve with the external", + "network E in my second step.", + "And notice that I can compute RTH and VTH for the Thevenin", + "equivalent using the discussion from a few minutes", + "ago, where I can measure it by measuring the open circuit", + "voltage and the effective resistance of the network with", + "all sources turned off.", + "Or I can also compute it by using superposition and", + "turning off each of the voltages one by one.", + "I can do it in either way.", + "So this is the Thevenin method.", + "Again, as a first step, I replace the network N with a", + "Thevenin equivalent, and then I solve for the external", + "network, E.", + "Now you might wonder, when is this useful?", + "So it turns out that in many cases where all you're", + "interested in is some value, V for example, and you don't", + "really care about what's going on inside this horrendous", + "network N, then you can simplify your life", + "tremendously by replacing that entire network with its", + "Thevenin equivalent, and then solving the circuit for the", + "voltage V based on that Thevenin equivalent.", + "Again, this is a process where we divide up the problem into", + "two simpler components, finding a Thevenin and then", + "solving the resulting circuit.", + "So let us now move on to an example and go to our old", + "faithful little circuit here.", + "And in this example, let us say that my goal here is to", + "find out the current, I1.", + "All I care about is to find out the current, I1.", + "Now of course I can go ahead and apply the Norton", + "method and do it.", + "But let us say that in this case I want to apply the", + "Thevenin method and use this as an example, and I'm going", + "to show you how simple it can get.", + "So to apply the Thevenin method, remember the first", + "part was to identify some sub-network and replace that", + "by its Thevenin equivalent.", + "So what I'm going to do is I'm going to identify this network", + "here as the arbitrary network N whose Thevenin equivalent", + "I'm going to find.", + "And then I'm going to view the network on the left-hand side,", + "the voltage and resistance, as the network E. And the reason", + "I'm going to do that is, notice that if I replace", + "network N with a Thevenin equivalent, which would be", + "simply a resistance and a voltage, notice that the", + "resulting circuit would be very simple to analyze,", + "because it would have pair of voltages and a pair of", + "resistances in series.", + "Let me we go ahead and find the Thevenin equivalent for", + "network one in step one of the Thevenin method.", + "So I'm going to replace network N by its Thevenin", + "equivalent.", + "So my network E is going to stay the same.", + "So E hasn't changed.", + "I'm trying to figure out the value of I1.", + "And I'm going to replace the network N with this Thevenin", + "equivalent.", + "So the Thevenin equivalent will fit in here into this", + "box, and let me draw the Thevenin pattern, just to be", + "clear, where this is R Thevenin", + "and this is V Thevenin.", + "And we'll replace network N with its Thevenin equivalent,", + "and in order to do that, I need to find all the values of", + "RTH and VTH.", + "And let me go ahead and do that next.", + "Continuing with step one of the Thevenin method, I have my", + "network N. And I need to find out VTH and RTH for that", + "network N. And again, as a reminder, this is what I have", + "for VTH and RTH.", + "So let me first find out the VTH.", + "And as I told you earlier, VTH is simply the open circuit", + "voltage of the network N. So how do I find out what the", + "open circuit voltage of that network N is?", + "Well, it's pretty straightforward.", + "Let me draw the network here.", + "Let's have an R2 here, and I have a current here.", + "And the open circuit voltage is my Thevenin voltage, VTH.", + "So here's your simple pattern.", + "I have a current I that is flowing into a resistance R2.", + "And so therefore VTH is simply I times R2.", + "So that gives me VTH.", + "So the second step, I need to find out RTH.", + "And the way I'm going to find out RTH is I'm going to turn", + "off all the independent sources inside network N, and", + "then measure the resistance looking in.", + "So this was my network from before.", + "This corresponds to this network.", + "I'll do the same now.", + "So I'm going to put my network in there.", + "And the difference is that I'm going to turn off all the", + "voltages and currents that are", + "independent inside that network.", + "So as I draw it out, R2 stays the same.", + "But here, what I'm going to do is I'm going to turn off my", + "current source and open-circuit that.", + "So I'm going to turn off my current source, and so now,", + "RTH will simply be the resistance looking in.", + "That is easy enough to do.", + "So RTH is simply R2.", + "So there you have it.", + "I've computed VTH and RTH, and that lets me develop my", + "Thevenin network, and I'm ready for step two.", + "So as I said earlier, VTH and RTH are given", + "by these two values.", + "And what I'm going to do is I'm going to replace the", + "network N with its Thevenin equivalent.", + "Network E stays the same.", + "I show that here.", + "That hasn't changed.", + "But now what I'm going to do is I'm going to replace the", + "network N with its Thevenin equivalent like so.", + "But I get the RTH in series with the VTH, and the VTH is", + "given by IR2 and RTH is given by R2.", + "So in step two, I now need to solve with the external", + "network E applied to the Thevenin equivalent network", + "that as replaced the original network N. So this is, again,", + "a very simple circuit, and recall all that I", + "cared about was I1.", + "And so, let me let you think for a couple of seconds about", + "what the value of I1 is before I go and do it myself." + ] +} \ No newline at end of file