{
  "start": [
    0, 
    3780, 
    5290, 
    9590, 
    13370, 
    13735, 
    15275, 
    16740, 
    19790, 
    23420, 
    26470, 
    28560, 
    31630, 
    33770, 
    35320, 
    36750, 
    38390, 
    41660, 
    43720, 
    46740, 
    47805, 
    49920, 
    52170, 
    53540, 
    56530, 
    59350, 
    63350, 
    66470, 
    68440, 
    69220, 
    71320, 
    72870, 
    78300, 
    79890, 
    82470, 
    85670, 
    90720, 
    93660, 
    97005, 
    98280, 
    102090, 
    103460, 
    107090, 
    108040, 
    110700, 
    112510, 
    117400, 
    121890, 
    124450, 
    130229, 
    133180, 
    140010, 
    142500, 
    143580, 
    150010, 
    152720, 
    159180, 
    161330, 
    165510, 
    171270, 
    173750, 
    177000, 
    179340, 
    181273, 
    182400, 
    188140, 
    189210, 
    192730, 
    199620, 
    206460, 
    208220, 
    211810, 
    214510, 
    219790, 
    221440, 
    223910, 
    224950, 
    226060, 
    231860, 
    232940, 
    237990, 
    240450, 
    242470, 
    244760, 
    246470, 
    248420
  ], 
  "end": [
    3780, 
    5290, 
    9590, 
    13370, 
    13735, 
    15275, 
    16740, 
    19790, 
    23420, 
    26470, 
    28560, 
    31630, 
    33770, 
    35320, 
    36750, 
    38390, 
    41660, 
    43720, 
    46740, 
    47805, 
    49920, 
    52170, 
    53540, 
    56530, 
    59350, 
    63350, 
    66470, 
    68440, 
    69220, 
    71320, 
    72870, 
    78300, 
    79890, 
    82470, 
    85670, 
    90720, 
    93660, 
    97005, 
    98280, 
    102090, 
    103460, 
    107090, 
    108040, 
    110700, 
    112510, 
    117400, 
    121890, 
    124450, 
    130229, 
    133180, 
    140010, 
    142500, 
    143580, 
    150010, 
    152720, 
    159180, 
    161330, 
    165510, 
    171270, 
    173750, 
    177000, 
    179340, 
    181273, 
    182400, 
    188140, 
    189210, 
    192730, 
    196700, 
    206460, 
    208220, 
    211810, 
    214510, 
    219790, 
    221440, 
    223910, 
    224950, 
    226060, 
    231860, 
    232940, 
    237990, 
    240450, 
    242470, 
    244760, 
    246470, 
    248420, 
    249670
  ], 
  "text": [
    "SPEAKER 1: We just learned the fundamental rules of", 
    "electrical circuits.", 
    "For example, if we have a circuit like this, which is", 
    "called a bridge and which has a voltage source and five", 
    "resistors--", 
    "SPEAKER 2: And I'll show the circuit in lecture.", 
    "SPEAKER 1: That's right.", 
    "We had a bunch of voltage current constraints, one for", 
    "each of the branches, each of the elements in the network.", 
    "For example, this one, the voltage across it is the", 
    "voltage intrinsic to it.", 
    "And we have Kirchoff's Current Laws, one for each of the", 
    "possible nodes in the network.", 
    "So that's four of them here.", 
    "It turns out one of them is redundant.", 
    "It can be derived from the others.", 
    "And we have Kirchoff Voltage Laws, which are some of the", 
    "voltages around the loop is zero.", 
    "And I have four of them written down here, and only", 
    "three of them are independent.", 
    "But we can have many more because there's a loop I", 
    "didn't show, which is the one that looks like this, for", 
    "example, OK?", 
    "And the other thing we have is that some of the powers on the", 
    "network entering each the elements is zero.", 
    "So there's no power gained or lost. This is a general method", 
    "of solving all circuit problems. Unfortunately, even", 
    "for a simple circuit like this, we have a mess of", 
    "equations here.", 
    "This is not a good idea.", 
    "SPEAKER 2: So in the next lecture, what Anant will show", 
    "you is a much more coherent, a much better organized", 
    "technique for solving these circuits.", 
    "So again, if we circle this circuit--", 
    "this is the same brood circuit Anant showed in the lecture--", 
    "we have six resistors, one, two, three, four nodes.", 
    "And what we do is we take each of these nodes and for those", 
    "nodes we'll write Kirchoff's Current Law.", 
    "And that's called nodal analysis.", 
    "So step zero is we pick one of these nodes and we label that", 
    "node as ground.", 
    "And labeling it ground just says the voltage on", 
    "that node is zero.", 
    "SPEAKER 1: The potential on that node is zero.", 
    "Voltages are differences of potential.", 
    "SPEAKER 2: Then we take a node, such as b.", 
    "And for that node, b, we write down an equation that says the", 
    "currents going into that node are o0.", 
    "So IR1 is plus IR2 plus IR3 is equal to zero.", 
    "We take this node, d, where we also write down Kirchoff's", 
    "Current Law, IR3 plus IR4 plus IR5 is equal to zero.", 
    "And at that point, we substitute", 
    "in for those voltages.", 
    "So when we have IR3, that's just b minus d over R3.", 
    "That's the current going into it.", 
    "For R5 over here, we have just d--", 
    "IS is 0 minus d.", 
    "So that's just minus d over R5.", 
    "And for IR4, we have a minus d over R4.", 
    "So we have an equation like this.", 
    "SPEAKER 1: So these labels, a, b and d, are within node", 
    "potentials, OK?", 
    "SPEAKER 2: We do the same thing over here for--", 
    "SPEAKER 1: Right, yes.", 
    "SPEAKER 2: We do the same thing over here for IR2 is--", 
    "SPEAKER 1: It's IR1.", 
    "SPEAKER 2: IR1 is a minus b over R1.", 
    "IR3 is d minus b over R3.", 
    "And finally, IR2 is minus b over R2.", 
    "So now we have two equations.", 
    "And the last thing that we do is we label this node a to", 
    "have the voltage v. We say a is equal to v.", 
    "Since this is a zero, instead of a, it's v, we make that", 
    "substitution everywhere here.", 
    "We have two equations, two unknowns.", 
    "We solve it.", 
    "And that gives us our answer.", 
    "SPEAKER 1: So the equations are b and d because all the", 
    "A's are substituted for.", 
    "And all of the KCLs that were written with the KCLs for some", 
    "of the currents entering the node is zero.", 
    "You could have equally written them as some of the currents", 
    "leaving the node as zero and get the same answer because", 
    "that would just multiply everything by minus 1.", 
    "SPEAKER 2: So you'll see this next week.", 
    "That's just a preview of coming attractions."
  ]
}