266 lines
6.3 KiB
Plaintext
266 lines
6.3 KiB
Plaintext
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"text": [
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"SPEAKER 1: We just learned the fundamental rules of",
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"electrical circuits.",
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"For example, if we have a circuit like this, which is",
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"called a bridge and which has a voltage source and five",
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"resistors--",
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"SPEAKER 2: And I'll show the circuit in lecture.",
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"SPEAKER 1: That's right.",
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"We had a bunch of voltage current constraints, one for",
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"each of the branches, each of the elements in the network.",
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"For example, this one, the voltage across it is the",
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"voltage intrinsic to it.",
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"And we have Kirchoff's Current Laws, one for each of the",
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"possible nodes in the network.",
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"So that's four of them here.",
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"It turns out one of them is redundant.",
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"It can be derived from the others.",
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"And we have Kirchoff Voltage Laws, which are some of the",
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"voltages around the loop is zero.",
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"And I have four of them written down here, and only",
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"three of them are independent.",
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"But we can have many more because there's a loop I",
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"didn't show, which is the one that looks like this, for",
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"example, OK?",
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"And the other thing we have is that some of the powers on the",
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"network entering each the elements is zero.",
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"So there's no power gained or lost. This is a general method",
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"of solving all circuit problems. Unfortunately, even",
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"for a simple circuit like this, we have a mess of",
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"equations here.",
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"This is not a good idea.",
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"SPEAKER 2: So in the next lecture, what Anant will show",
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"you is a much more coherent, a much better organized",
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"technique for solving these circuits.",
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"So again, if we circle this circuit--",
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"this is the same brood circuit Anant showed in the lecture--",
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"we have six resistors, one, two, three, four nodes.",
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"And what we do is we take each of these nodes and for those",
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"nodes we'll write Kirchoff's Current Law.",
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"And that's called nodal analysis.",
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"So step zero is we pick one of these nodes and we label that",
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"node as ground.",
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"And labeling it ground just says the voltage on",
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"that node is zero.",
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"SPEAKER 1: The potential on that node is zero.",
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"Voltages are differences of potential.",
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"SPEAKER 2: Then we take a node, such as b.",
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"And for that node, b, we write down an equation that says the",
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"currents going into that node are o0.",
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"So IR1 is plus IR2 plus IR3 is equal to zero.",
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"We take this node, d, where we also write down Kirchoff's",
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"Current Law, IR3 plus IR4 plus IR5 is equal to zero.",
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"And at that point, we substitute",
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"in for those voltages.",
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"So when we have IR3, that's just b minus d over R3.",
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"That's the current going into it.",
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"For R5 over here, we have just d--",
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"IS is 0 minus d.",
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"So that's just minus d over R5.",
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"And for IR4, we have a minus d over R4.",
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"So we have an equation like this.",
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"SPEAKER 1: So these labels, a, b and d, are within node",
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"potentials, OK?",
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"SPEAKER 2: We do the same thing over here for--",
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"SPEAKER 1: Right, yes.",
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"SPEAKER 2: We do the same thing over here for IR2 is--",
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"SPEAKER 1: It's IR1.",
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"SPEAKER 2: IR1 is a minus b over R1.",
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"IR3 is d minus b over R3.",
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"And finally, IR2 is minus b over R2.",
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"So now we have two equations.",
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"And the last thing that we do is we label this node a to",
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"have the voltage v. We say a is equal to v.",
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"Since this is a zero, instead of a, it's v, we make that",
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"substitution everywhere here.",
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"We have two equations, two unknowns.",
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"We solve it.",
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"And that gives us our answer.",
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"SPEAKER 1: So the equations are b and d because all the",
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"A's are substituted for.",
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"And all of the KCLs that were written with the KCLs for some",
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"of the currents entering the node is zero.",
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"You could have equally written them as some of the currents",
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"leaving the node as zero and get the same answer because",
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"that would just multiply everything by minus 1.",
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"SPEAKER 2: So you'll see this next week.",
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"That's just a preview of coming attractions."
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]
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} |