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css/application.css
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"text": [
"SPEAKER 1: All right.",
"So v1 here is simply the difference between v0 and e1.",
"So v1 is simply v0 minus e1.",
"That's it.",
"What about i1?",
"That is pretty simple, too.",
"i1 is simply v1 divide by r1.",
"And because v1 is v0 minus e1, I can replace v1 by v0 minus",
"e1 and divide by r1.",
"That gives me i1.",
"So in this manner, I can go ahead and find all the vi's",
"and ii's very straightforwardly from the",
"known voltages.",
"So most often when we analyze circuits, we just go ahead and",
"find the e's-- the known voltages--",
"because we know we can very quickly find all the branch",
"voltages and currents.",
"And so, we often stop at the known voltage step."
]
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"text": [
"SPEAKER 1: Well, it turns out that I don't need a variable",
"there because of the trick that I used in picking my",
"ground node.",
"By picking my ground node where it was, notice that the",
"voltage at this node is simply v0, because this node is",
"connected to ground by a voltage source.",
"And so the voltage source would hold the voltage of that",
"node at v0.",
"So I directly have the voltage of that node.",
"So right there I've done my second step.",
"So that's my step two of node analysis.",
"So let's move on and start off with step",
"three of node analysis.",
"All right?",
"Step three would be to write KCL for the nodes-- on each of",
"the nodes-- e1 and e2 here, which are my unknowns.",
"I'm going to write KCL for these nodes, and I am going to",
"substitute device laws and KVL in dividing the current that",
"leaves those nodes.",
"But also remember that as I work with currents, and sum",
"the currents for KCL, I'll simply use my usual",
"convention, which is sum the currents leaving a node always",
"so I don't make mistakes.",
"Now again, for another piece of convenience, I'm going to",
"use conductances.",
"So the variable I have is resistance.",
"1 by that resistance is the conductance, since I would",
"just use that to make my algebra a little simpler.",
"So let's get started.",
"Let's start with node e1.",
"And I'm going to write KCL at node e1.",
"Now, with KCL, notice that I'm going to follow my usual",
"convention to avoid mistakes.",
"I'm going to add up the currents that leave a node so",
"that I don't make mistakes.",
"So let's go ahead and start.",
"Let me start with KCL at e1.",
"So if you look at e1, what is the current that is going up",
"in that direction?",
"I know the node voltage here is e1.",
"I know the voltage of this node is v0.",
"So can you tell me what the current is going up?",
"Let me pause for a second so that you can think about it.",
"And then I'll go back and do it for you."
]
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"text": [
"SPEAKER 1: Our third method is going to be the node method.",
"This method is going to be the most important method that we",
"learn, and you can apply it to all the circuits that you're",
"going to see.",
"This method is going to be a very specific application of",
"the KVL/KCL method.",
"This method has five steps.",
"The first step would be you go and select a reference node--",
"we call that a ground node--",
"represented by an inverted T symbol.",
"And you're going to measure all our voltages with",
"reference to this ground node.",
"The second step.",
"We label all the voltages of the remaining nodes with",
"respect to ground.",
"And these will be our primary unknowns.",
"As a third step, we will write KCL for all the nodes, leading",
"out the ground node.",
"And while writing KCL, we will apply a cool trick.",
"So KCL involves currents.",
"But notice that your primary variables",
"are your node voltages.",
"But KCL involves current, so what we will do is in step",
"three, we will derive the current, in terms of the node",
"voltages, and directly apply the element relationship",
"without actually having to write down",
"any specific current.",
"Then we go and solve for the node",
"voltages as our step four.",
"And finally, we go and back solve for the branch voltages",
"and branch currents.",
"Notice that for circuit analysis, our goal is to find",
"branch voltages and currents, and so to the extent that you",
"need to know all the branch voltages and currents, you can",
"go ahead and find them.",
"The node analysis method is the workhorse of our industry",
"and the workhorse of 6.002x.",
"And so you will be using it all over the place.",
"It's a very, very important method.",
"Let's get started.",
"And for this method, I'm going to use our",
"old faithful circuit.",
"For fun, I'm going to add a extra current source, I1, to",
"our circuit.",
"Notice that we now have seven elements in the circuit.",
"And with seven elements, the number of equations is going",
"to be completely unwieldy.",
"And so you will notice that with the node method, you will",
"be amazed that at the end, we will have to",
"solve only two equations.",
"Watch and see.",
"So as the first step of the node method, I have to select",
"the ground node.",
"Now, in general, you can select any node as the ground,",
"because voltages are always measured with",
"respect to a point.",
"There are differences in potentials between a pair of",
"points, so you can select any node as the ground.",
"But in general, to simplify our lives, I'd recommend using",
"a couple of rules to pick a ground node to",
"simplify the analysis.",
"The first thing to do is to find a node which has the",
"largest number of edges coming to it.",
"And in our circuit here, this node here, which connects R to",
"R5, and the current and voltage sources has the",
"largest number of edges.",
"So that seemed like a good candidate.",
"A second thing you can look at is look for a node that has",
"many of the sources connected to it.",
"And in this case, it does happen that the same node has",
"the voltage source also connected",
"to it with one terminal.",
"So let me go ahead and pick that as my ground node.",
"So let me go ahead and mark that as my ground node.",
"This will be my ground, and I mark it",
"with my ground terminal.",
"So this is step one.",
"Now, let's apply step two.",
"Step two will be label node voltages with respect to the",
"ground node.",
"So what are my nodes?",
"So I have a node here.",
"That's one node.",
"Let me label the node voltage with respect to ground as E1.",
"So if I take this as my ground voltage and",
"take that as a zero--",
"so the voltage at this node here is going to be E1 with",
"respect to the ground.",
"Let me pick this node here as E2 with respect to ground.",
"Finally, I have a third node here.",
"And what can you say about the voltage at that node?",
"Let me pause for a second while you think about it, and",
"then I will continue.",
"So what do you think the voltage is at that node?",
"Do I need a variable there?"
]
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"text": [
"SPEAKER 1: All right, so to do KCL at e2, let's start with",
"the current leaving this node.",
"Remember, my usual habit is to sum the",
"nodes leaving the node.",
"So the current heading in this direction will be e2 minus e1",
"divided by R3.",
"So current going left from that node will be e2 minus e1",
"divided by R3 or multiplied by G3.",
"Then the current going up will be e2 minus V0 times G4.",
"And the current leaving the node and going down",
"will be e2 times G5.",
"Have I missed anything?",
"Aha, there is a current here that's coming into the node.",
"And so therefore, the current leaving the mode is minus I1.",
"And all of that sums up to zero.",
"There you have it.",
"So I've written KCL for the two nodes.",
"And I've substituted the device laws as I've been",
"writing it so I don't have this",
"intermediate current variable.",
"So just stare at the beauty of this.",
"Notice that I have two equations, one and two, and I",
"have two variables, e1 and e2, two unknowns and two equations",
"and that's it.",
"OK, so let me go on to step four of the node method.",
"The step four of the node method is simply to go ahead",
"and solve for the node voltages, e1 and e2.",
"So I have my two equations which reflect the KCL at node",
"e1 and KCL at e2.",
"So now it's simply juggling it on with some math and trying",
"to collect all the coefficients of e1 and those",
"of e2, collect them all and just write",
"them a little cleanly.",
"So let me move all the constant terms to the",
"right-hand side.",
"And I will move the variables, or the unknowns, to the",
"left-hand hand side.",
"So let me start with e1.",
"So notice that e1, I multiplied by G1, so",
"I write that down.",
"Multiply by G3, so I write that down.",
"And multiply by G2, so I write that down too.",
"So I get e1 times G1 plus G3 plus G2.",
"And then I collect the terms in e2.",
"And there's only one here, which is minus G3.",
"And the constant terms are here, V0 G1.",
"And I'm going to move that to the right-hand side and write",
"that down as V0 G1.",
"For the next set of steps, I go ahead and do e1 for the",
"next equation.",
"I get minus G3.",
"And then for e2, I go ahead and get a G5, and I get a G4,",
"and I get a G3.",
"So it's G3, G4, and a G5.",
"And I can move the constant terms, which is V0 G4, and I",
"want the right-hand side.",
"And in this case, they both become positive as they move",
"to the right.",
"And I get a I1 here.",
"Good, there you go.",
"So I end up with two equations and two unknowns.",
"And notice I have by e1 times something plus e2 times",
"something equals a constant.",
"And then again, that e1 times something plus e2 times",
"something is another constant.",
"So I two equations and two unknowns.",
"And see how remarkably simple this is.",
"This is basic high school math to solve a pair of",
"simultaneous equations in order to get the answer.",
"And just to be a complete here, let me go ahead and",
"complete it for you.",
"So supposing in step four number four you've gone and",
"solved for the node method, and by solving the node method",
"you get the values of e1 and e2.",
"So let's say you've gone and solved the simultaneous",
"equations for step four and you have e1 and e2.",
"Then, to complete your circuit analysis you need to find the",
"branch voltages.",
"And so you can go ahead and find all the v-i's and i-i's.",
"So in this case, one of my branch voltages is v1 i1.",
"So I just do a couple of quick examples just to show you that",
"it's pretty simple.",
"So what is v1 here?",
"Well let me pause and have you do it."
]
}
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subs/UwpSwe_RIbM.srt.sjson 0 → 100644
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"start": [],
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"text": []
}
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subs/XgSOO1sfsa4.srt.sjson 0 → 100644
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"text": [
"SPEAKER 1: OK, let's now work on the second method of",
"circuit analysis.",
"This is actually a very simple method.",
"And oftentimes when you're applying some of the more",
"sophisticated methods, it is helpful to apply these methods",
"as some of the partial steps.",
"You can find more about this method and the KVL KCL method",
"in chapter two of the textbook.",
"So this method is very simple.",
"If you have a set of resistors in series, R1 through RN, then",
"you can write up an equivalent resistor whose resistance is",
"equal to the sum of the individual resistances.",
"Now you can also do a complimentary circuit.",
"You can make a set of conductances.",
"Notice that G is our nomenclature for conductance.",
"So G1, for example, is 1 divided by R1 and so on, so",
"G's a conductance.",
"So when I have a set of conductances in parallel, then",
"I can add them all up and replace them with a resulting",
"conductance given by G1 plus G2 plus G3 dot dot dot GN,",
"where G1 equals 1 by RI is a conductance.",
"Another simple thing to remember is when you have two",
"resistances in parallel, let's say R1 and R2, the equivalent",
"resistance is given by R1 R2 divide by R1 plus R2.",
"This is just a special case for two resistors.",
"Let's continue one with element combinations rules.",
"In case C is when I have two voltage sources in parallel.",
"Let's call them V1 and V2.",
"Then I can replace them with a single voltage source whose",
"voltage is given by V1 plus V2.",
"I can get the current based circuit in a similar manner.",
"So let's say I have two current sources in parallel,",
"I1 in parallel with I2.",
"Then I can replace them with a single current source whose",
"current is I1 plus I2.",
"In this example, I would like to use element combination",
"rules to solve for the following situation.",
"So I have a little circuit here with a voltage source of",
"three resistors.",
"And let's say I care about finding the current I through",
"that branch.",
"So how do I go about doing it?",
"So let's start applying element competition rules.",
"As a first step, let me combine these two resistances.",
"And so I get the same voltage source, my resistance R1 here.",
"But in place of R2 and R3, I get the combination of",
"resistors given by R2 R3 3 divide by R2 plus R3.",
"Now as soon as I get that, I now have two resistances in",
"series, so I can sum them up very quickly like so.",
"And I can get a single resistance here, R, which is",
"the sum of R1 plus R2 R3 divide by R2 plus R3.",
"So now notice that this was my current that I needed to find.",
"And I was the current I needed to find.",
"So I brought this down to a very simple pattern.",
"And so I can very quickly write I is simply given by V",
"divided by R.",
"Now the textbook in this particular section gives you a",
"lot more interesting examples of how you can use intuitive",
"analysis to analyze many, many circuits like this.",
"And I would encourage you to go and read that section",
"that's part of section two."
]
}
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subs/t24YP3JIKI8.srt.sjson 0 → 100644
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"text": [
"SPEAKER 1: All right.",
"So I can apply the KVL rule.",
"The KVL rule simply says that I can take the difference in",
"the node voltages.",
"And then applying the element rule, I can divide by R1 to",
"get the current going up.",
"So the current going up is simply E1 minus V0, which is",
"the voltage difference between these two points.",
"And I can divide that by R1 to get the current going up.",
"And dividing by R1 is the same as multiplying by the",
"conductance, G1.",
"OK.",
"Next.",
"What is the current going in this direction?",
"The current going in that direction is simply E1 minus",
"E3 divided by R3, or multiplied by the",
"conductance, G3.",
"And finally, I can figure out the current going down, which",
"is simply E1 minus 0, which is the ground",
"potential, times G2.",
"And that sums to 0 by KCL.",
"OK.",
"Next let me write down KCL at the node two.",
"So let me give you some practice, and let me pause",
"while you think about doing it yourself.",
"And then I'll go ahead and do it."
]
}
\ No newline at end of file
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