[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.01,0:00:03.39,Default,,0000,0000,0000,,>> All right. In our previous video,
Dialogue: 0,0:00:03.39,0:00:08.75,Default,,0000,0000,0000,,we found that the Thevenin\Nequivalent voltage, V_Th,
Dialogue: 0,0:00:08.75,0:00:16.29,Default,,0000,0000,0000,,was equal to 6.25 angle 51.34 degrees.
Dialogue: 0,0:00:16.29,0:00:19.80,Default,,0000,0000,0000,,Once again, I'm going to be\Nusing this shorthand notation
Dialogue: 0,0:00:19.80,0:00:24.75,Default,,0000,0000,0000,,of representing the polar coordinates\Nof the impedances of the phasors
Dialogue: 0,0:00:24.75,0:00:30.30,Default,,0000,0000,0000,,as opposed to writing 6.25e to the j51.34.
Dialogue: 0,0:00:30.30,0:00:34.18,Default,,0000,0000,0000,,All right. With the Thevenin voltage,
Dialogue: 0,0:00:35.51,0:00:38.91,Default,,0000,0000,0000,,we need now simply to determine
Dialogue: 0,0:00:38.91,0:00:44.06,Default,,0000,0000,0000,,the Thevenin equivalent impedance
Dialogue: 0,0:00:44.06,0:00:47.15,Default,,0000,0000,0000,,and we're going to do that\Neach of three different ways.
Dialogue: 0,0:00:47.15,0:00:52.07,Default,,0000,0000,0000,,This first method is what we'll refer\Nto as the Equivalent Impedance method.
Dialogue: 0,0:00:52.07,0:00:59.64,Default,,0000,0000,0000,,It works when we have\Nonly independent sources or no sources.
Dialogue: 0,0:00:59.64,0:01:02.06,Default,,0000,0000,0000,,This equivalent impedance method\Nthat we're going to show first
Dialogue: 0,0:01:02.06,0:01:07.04,Default,,0000,0000,0000,,does not work if the circuit you're\Nanalyzing has dependent sources.
Dialogue: 0,0:01:07.04,0:01:14.63,Default,,0000,0000,0000,,So, this approach requires us to deactivate\Nany independent sources present.
Dialogue: 0,0:01:14.63,0:01:16.67,Default,,0000,0000,0000,,In this case, there's\Nan independent voltage source here
Dialogue: 0,0:01:16.67,0:01:18.77,Default,,0000,0000,0000,,which we deactivate by turning it to zero
Dialogue: 0,0:01:18.77,0:01:22.74,Default,,0000,0000,0000,,and thus replacing it with a short circuit.
Dialogue: 0,0:01:22.74,0:01:27.59,Default,,0000,0000,0000,,Then, looking back into\Nthe circuit from the terminals AB
Dialogue: 0,0:01:27.59,0:01:30.86,Default,,0000,0000,0000,,and determining what the equivalent\Nimpedance is that we would see
Dialogue: 0,0:01:30.86,0:01:32.74,Default,,0000,0000,0000,,looking back in that way.
Dialogue: 0,0:01:32.74,0:01:37.91,Default,,0000,0000,0000,,Well, hopefully you can see pretty\Neasily that with the source deactivated-
Dialogue: 0,0:01:37.91,0:01:39.14,Default,,0000,0000,0000,,replaced with short-circuit,
Dialogue: 0,0:01:39.14,0:01:42.08,Default,,0000,0000,0000,,it brings this capacitor and\Nthis resistor in parallel,
Dialogue: 0,0:01:42.08,0:01:48.83,Default,,0000,0000,0000,,-and that parallel combination is\Nin series with the j50-Ohm resistor
Dialogue: 0,0:01:48.83,0:01:53.84,Default,,0000,0000,0000,,such that the impedance seen\Nlooking back into these terminals,
Dialogue: 0,0:01:53.84,0:02:01.54,Default,,0000,0000,0000,,Z Thevenin, will equal Z parallel\Nplus the j50-Ohm inductor.
Dialogue: 0,0:02:01.54,0:02:05.60,Default,,0000,0000,0000,,So, Z parallel is equal to
Dialogue: 0,0:02:05.60,0:02:13.42,Default,,0000,0000,0000,,20 times minus j25 divided by 20 minus j25,
Dialogue: 0,0:02:13.42,0:02:24.96,Default,,0000,0000,0000,,which turns out to equal\N12.2 minus j9.8 Ohms.
Dialogue: 0,0:02:24.96,0:02:29.83,Default,,0000,0000,0000,,So finally, Z Thevenin then is equal to Zp;
Dialogue: 0,0:02:29.83,0:02:38.12,Default,,0000,0000,0000,,12.2 minus j9.8 plus the j50,
Dialogue: 0,0:02:38.12,0:02:47.20,Default,,0000,0000,0000,,and that then equals 12.2 plus j40.2 Ohms.
Dialogue: 0,0:02:48.53,0:02:51.53,Default,,0000,0000,0000,,Z Thevenin, bringing it up here,
Dialogue: 0,0:02:51.53,0:02:56.22,Default,,0000,0000,0000,,then rewriting it just to show what\Nwe've got to show our incomplete model.
Dialogue: 0,0:02:56.22,0:03:05.06,Default,,0000,0000,0000,,Our complete model involves the Z Thevenin\Nequaling 12.2 plus j40.2 ohms
Dialogue: 0,0:03:05.06,0:03:10.73,Default,,0000,0000,0000,,and our claim then is that\Nthis Thevenin equivalent circuit
Dialogue: 0,0:03:10.73,0:03:13.91,Default,,0000,0000,0000,,has the same terminal characteristics\Nat the AB terminals
Dialogue: 0,0:03:13.91,0:03:17.88,Default,,0000,0000,0000,,as our original more complicated circuit.