[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.92,0:00:03.67,Default,,0000,0000,0000,,>> Our third and final method for finding
Dialogue: 0,0:00:03.67,0:00:07.00,Default,,0000,0000,0000,,the Thevenin equivalent\Nimpedance of the circuit,
Dialogue: 0,0:00:07.00,0:00:12.82,Default,,0000,0000,0000,,involves applying an external source\Nto the terminals of our circuit,
Dialogue: 0,0:00:12.82,0:00:18.13,Default,,0000,0000,0000,,after deactivating\Nthe any independent sources.
Dialogue: 0,0:00:18.13,0:00:21.93,Default,,0000,0000,0000,,So this circuit that we're\Nfinding the Thevenin circuit for,
Dialogue: 0,0:00:21.93,0:00:27.08,Default,,0000,0000,0000,,involved or has a single\Nindependent voltage source.
Dialogue: 0,0:00:27.08,0:00:29.62,Default,,0000,0000,0000,,We're going to deactivate\Nthat independent source
Dialogue: 0,0:00:29.62,0:00:32.22,Default,,0000,0000,0000,,again by replacing it with a short-circuit.
Dialogue: 0,0:00:32.22,0:00:40.76,Default,,0000,0000,0000,,This method then involves applying\Nan external voltage source just V,
Dialogue: 0,0:00:40.76,0:00:43.95,Default,,0000,0000,0000,,call it V_ex for external,
Dialogue: 0,0:00:43.95,0:00:46.97,Default,,0000,0000,0000,,which would then cause a current to flow.
Dialogue: 0,0:00:46.97,0:00:49.18,Default,,0000,0000,0000,,We'll call it I_ex,
Dialogue: 0,0:00:49.18,0:00:50.87,Default,,0000,0000,0000,,for the external current of the current,
Dialogue: 0,0:00:50.87,0:00:53.05,Default,,0000,0000,0000,,is due to this external voltage source,
Dialogue: 0,0:00:53.05,0:00:57.01,Default,,0000,0000,0000,,and Z Thevenin then is going to equal,
Dialogue: 0,0:00:57.01,0:01:02.96,Default,,0000,0000,0000,,the ratio of V_ex to I_ex.
Dialogue: 0,0:01:02.96,0:01:08.84,Default,,0000,0000,0000,,This method works under any circumstances,
Dialogue: 0,0:01:08.84,0:01:12.72,Default,,0000,0000,0000,,whether you have dependent\Nor independent sources.
Dialogue: 0,0:01:12.72,0:01:14.88,Default,,0000,0000,0000,,This third method will work.
Dialogue: 0,0:01:14.88,0:01:17.00,Default,,0000,0000,0000,,Sometimes it gets to be\Nalgebraically a little bit
Dialogue: 0,0:01:17.00,0:01:20.27,Default,,0000,0000,0000,,cumbersome involving multiple equations\Nand multiple unknowns,
Dialogue: 0,0:01:20.27,0:01:22.67,Default,,0000,0000,0000,,but it will always work.
Dialogue: 0,0:01:22.67,0:01:25.77,Default,,0000,0000,0000,,This method is equivalent to,
Dialogue: 0,0:01:25.77,0:01:29.31,Default,,0000,0000,0000,,and can maybe something of a visual,
Dialogue: 0,0:01:29.31,0:01:35.12,Default,,0000,0000,0000,,of a gasoline engine and an exhaust system.
Dialogue: 0,0:01:35.12,0:01:37.84,Default,,0000,0000,0000,,If you wanted to measure or to model,
Dialogue: 0,0:01:37.84,0:01:45.30,Default,,0000,0000,0000,,the back pressure due to\Nthe resistance of the exhaust system.
Dialogue: 0,0:01:45.30,0:01:47.86,Default,,0000,0000,0000,,This would be like turning off the engine,
Dialogue: 0,0:01:47.86,0:01:51.23,Default,,0000,0000,0000,,and then putting your mouth over\Nthe exhaust pipe and blowing
Dialogue: 0,0:01:51.23,0:01:54.53,Default,,0000,0000,0000,,into it and measuring\Nthe current that flows,
Dialogue: 0,0:01:54.53,0:01:57.80,Default,,0000,0000,0000,,then that resistance of\Nthe exhaust system would be
Dialogue: 0,0:01:57.80,0:02:01.49,Default,,0000,0000,0000,,equal to the pressure that\Nyou're pushing against it,
Dialogue: 0,0:02:01.49,0:02:04.42,Default,,0000,0000,0000,,divided by the amount of\Nair that flowed into it.
Dialogue: 0,0:02:04.42,0:02:06.83,Default,,0000,0000,0000,,So our Thevenin impedance will be,
Dialogue: 0,0:02:06.83,0:02:10.02,Default,,0000,0000,0000,,we're going to deactivate\Nthe source, the independent sources.
Dialogue: 0,0:02:10.02,0:02:11.69,Default,,0000,0000,0000,,If there were dependent sources in here,
Dialogue: 0,0:02:11.69,0:02:13.83,Default,,0000,0000,0000,,we would leave them active,
Dialogue: 0,0:02:13.96,0:02:18.94,Default,,0000,0000,0000,,and having deactivated\Nthe independent sources,
Dialogue: 0,0:02:18.94,0:02:21.73,Default,,0000,0000,0000,,pushing against this or applying a voltage,
Dialogue: 0,0:02:21.73,0:02:25.52,Default,,0000,0000,0000,,and taking the ratio of\Nthe voltage to the current.
Dialogue: 0,0:02:25.52,0:02:27.28,Default,,0000,0000,0000,,So here's our circuit then.
Dialogue: 0,0:02:27.28,0:02:28.55,Default,,0000,0000,0000,,We've deactivated the source,
Dialogue: 0,0:02:28.55,0:02:31.42,Default,,0000,0000,0000,,we're applying the external voltage source,
Dialogue: 0,0:02:31.42,0:02:35.39,Default,,0000,0000,0000,,and we need to do some algebra and write\Nsome equations that will allow us to
Dialogue: 0,0:02:35.39,0:02:39.95,Default,,0000,0000,0000,,come up with a ratio of the external\Nvoltage to the external current.
Dialogue: 0,0:02:39.95,0:02:43.00,Default,,0000,0000,0000,,With this circuit here,
Dialogue: 0,0:02:43.00,0:02:45.60,Default,,0000,0000,0000,,and with the source deactivated,
Dialogue: 0,0:02:45.60,0:02:47.50,Default,,0000,0000,0000,,we see now that this 20 ohm and
Dialogue: 0,0:02:47.50,0:02:51.58,Default,,0000,0000,0000,,the negative j25 ohm capacitor\Nare in parallel with each other.
Dialogue: 0,0:02:51.58,0:02:54.88,Default,,0000,0000,0000,,So let's call that Z parallel,
Dialogue: 0,0:02:54.88,0:03:00.04,Default,,0000,0000,0000,,and by reducing those to\Na parallel combination,
Dialogue: 0,0:03:00.04,0:03:01.82,Default,,0000,0000,0000,,we'll have these two,
Dialogue: 0,0:03:01.82,0:03:05.10,Default,,0000,0000,0000,,the parallel equivalent\Nin series with that,
Dialogue: 0,0:03:05.10,0:03:09.10,Default,,0000,0000,0000,,and we'll then be able to write\Nthe expression for the external current,
Dialogue: 0,0:03:09.10,0:03:12.14,Default,,0000,0000,0000,,will just be equal to this Thevenin\Nor this external voltage,
Dialogue: 0,0:03:12.14,0:03:16.45,Default,,0000,0000,0000,,divided by the series\Ncombination of those two,
Dialogue: 0,0:03:16.45,0:03:19.39,Default,,0000,0000,0000,,of this plus the parallel equivalent.
Dialogue: 0,0:03:19.39,0:03:23.15,Default,,0000,0000,0000,,So Z parallel is equal to,
Dialogue: 0,0:03:23.15,0:03:26.93,Default,,0000,0000,0000,,negative j25 times 20,
Dialogue: 0,0:03:26.93,0:03:31.58,Default,,0000,0000,0000,,divided by 20 minus j25,
Dialogue: 0,0:03:31.58,0:03:40.68,Default,,0000,0000,0000,,and that again works out\Nto be 12.2 minus j9.76.
Dialogue: 0,0:03:40.68,0:03:42.97,Default,,0000,0000,0000,,So we have then,
Dialogue: 0,0:03:42.97,0:03:46.54,Default,,0000,0000,0000,,just redrawing to make obvious\Nwhat we're doing here.
Dialogue: 0,0:03:46.54,0:03:50.20,Default,,0000,0000,0000,,You've got this inductor j50,
Dialogue: 0,0:03:50.90,0:03:54.27,Default,,0000,0000,0000,,and we have this equivalent impedance,
Dialogue: 0,0:03:54.27,0:04:00.43,Default,,0000,0000,0000,,of 12.2 minus j9.76.
Dialogue: 0,0:04:02.66,0:04:05.33,Default,,0000,0000,0000,,This is our external voltage,
Dialogue: 0,0:04:05.33,0:04:08.52,Default,,0000,0000,0000,,and there'll be\Nan external current flowing.
Dialogue: 0,0:04:09.61,0:04:13.92,Default,,0000,0000,0000,,We can now write an expression for I_ex.
Dialogue: 0,0:04:13.92,0:04:18.44,Default,,0000,0000,0000,,The external current is just\Nequal to the external voltage,
Dialogue: 0,0:04:18.44,0:04:20.95,Default,,0000,0000,0000,,divided by the sum of those,
Dialogue: 0,0:04:20.95,0:04:34.38,Default,,0000,0000,0000,,which is j50 plus 12.2 minus j9.76,
Dialogue: 0,0:04:34.38,0:04:39.94,Default,,0000,0000,0000,,and the ratio V_ex over I_ex then,
Dialogue: 0,0:04:39.94,0:04:42.73,Default,,0000,0000,0000,,can be gotten by multiplying\Nboth sides of the equation by
Dialogue: 0,0:04:42.73,0:04:46.75,Default,,0000,0000,0000,,this denominator and dividing\Nboth sides by I_ex, and we get then,
Dialogue: 0,0:04:46.75,0:04:51.43,Default,,0000,0000,0000,,that V_ex over I_ex is equal
Dialogue: 0,0:04:51.43,0:04:59.68,Default,,0000,0000,0000,,to 12.2 plus j40.2,
Dialogue: 0,0:04:59.68,0:05:05.69,Default,,0000,0000,0000,,and that of course is\Nour Thevenin equivalent voltage.
Dialogue: 0,0:05:05.69,0:05:07.25,Default,,0000,0000,0000,,So we've seen now,
Dialogue: 0,0:05:07.25,0:05:12.18,Default,,0000,0000,0000,,three different methods of\Ncalculating the Thevenin impedance,
Dialogue: 0,0:05:12.18,0:05:17.60,Default,,0000,0000,0000,,and which one works best becomes\Na matter of art and experience.
Dialogue: 0,0:05:17.60,0:05:19.55,Default,,0000,0000,0000,,You'll have some opportunities to do enough
Dialogue: 0,0:05:19.55,0:05:21.74,Default,,0000,0000,0000,,of these and you'll start to get a feel for
Dialogue: 0,0:05:21.74,0:05:27.75,Default,,0000,0000,0000,,the circumstances that make each of\Nthese different methods most applicable.