[Script Info]
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[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.42,Default,,0000,0000,0000,,>> In the next few videos, we're\Ngoing to extend the concepts of
Dialogue: 0,0:00:03.42,0:00:08.68,Default,,0000,0000,0000,,equivalent circuits into the phasor domain,
Dialogue: 0,0:00:08.68,0:00:14.20,Default,,0000,0000,0000,,in terms of impedances and\Nphasor voltages and phasor currents.
Dialogue: 0,0:00:14.20,0:00:16.54,Default,,0000,0000,0000,,So to do that,
Dialogue: 0,0:00:17.15,0:00:22.28,Default,,0000,0000,0000,,we're going to start by looking\Nat the source transformations,
Dialogue: 0,0:00:22.28,0:00:24.00,Default,,0000,0000,0000,,transforming a voltage source with
Dialogue: 0,0:00:24.00,0:00:30.25,Default,,0000,0000,0000,,a series impedance into a current source\Nwith a parallel impedance and back.
Dialogue: 0,0:00:30.25,0:00:32.93,Default,,0000,0000,0000,,Then we'll also extend the concept of
Dialogue: 0,0:00:32.93,0:00:38.83,Default,,0000,0000,0000,,Thevenin equivalent circuits to include\Nphasors and complex impedances.
Dialogue: 0,0:00:38.83,0:00:43.49,Default,,0000,0000,0000,,So by review, what we mean when we\Nsay two circuits are equivalent,
Dialogue: 0,0:00:43.49,0:00:52.05,Default,,0000,0000,0000,,we mean that they have in this case\Nthe same terminal characteristics.
Dialogue: 0,0:00:55.94,0:01:01.07,Default,,0000,0000,0000,,By that we mean that\Nan external circuit connected to
Dialogue: 0,0:01:01.07,0:01:05.27,Default,,0000,0000,0000,,a voltage source with a series\Nimpedance will experience
Dialogue: 0,0:01:05.27,0:01:10.61,Default,,0000,0000,0000,,the same voltage and current\Nas that same external circuit
Dialogue: 0,0:01:10.61,0:01:16.49,Default,,0000,0000,0000,,would experience if it were connected\Nto a parallel current source,
Dialogue: 0,0:01:16.49,0:01:20.41,Default,,0000,0000,0000,,connected in parallel with an impedance.
Dialogue: 0,0:01:20.41,0:01:25.07,Default,,0000,0000,0000,,Both instances, we're going to have\Nthe source impedance be the same value,
Dialogue: 0,0:01:25.07,0:01:27.32,Default,,0000,0000,0000,,and what we wanted to do is\Ndetermine the relationship between
Dialogue: 0,0:01:27.32,0:01:30.06,Default,,0000,0000,0000,,V sub s and I sub s.
Dialogue: 0,0:01:30.06,0:01:32.78,Default,,0000,0000,0000,,So that loads or
Dialogue: 0,0:01:32.78,0:01:34.46,Default,,0000,0000,0000,,external circuits connected to either
Dialogue: 0,0:01:34.46,0:01:36.64,Default,,0000,0000,0000,,of these would not be able\Nto tell the difference.
Dialogue: 0,0:01:36.64,0:01:39.20,Default,,0000,0000,0000,,So they have the same\Nterminal characteristics.
Dialogue: 0,0:01:39.20,0:01:50.49,Default,,0000,0000,0000,,That means same voltage and same current.
Dialogue: 0,0:01:51.01,0:01:59.60,Default,,0000,0000,0000,,To accomplish that, this load here\Nis going to experience the same V,
Dialogue: 0,0:01:59.60,0:02:02.27,Default,,0000,0000,0000,,what reference V12, the voltage from
Dialogue: 0,0:02:02.27,0:02:05.87,Default,,0000,0000,0000,,node one to node two in both the circuits.
Dialogue: 0,0:02:05.87,0:02:11.42,Default,,0000,0000,0000,,In other words, this V12 and\Nthis V12 will be the same.
Dialogue: 0,0:02:11.42,0:02:13.36,Default,,0000,0000,0000,,So to do that,
Dialogue: 0,0:02:13.36,0:02:16.20,Default,,0000,0000,0000,,we need to have the open-circuit voltage.
Dialogue: 0,0:02:16.20,0:02:19.07,Default,,0000,0000,0000,,The voltage that you would\Nexperience if there was
Dialogue: 0,0:02:19.07,0:02:22.28,Default,,0000,0000,0000,,no load connected here to be the same.
Dialogue: 0,0:02:22.28,0:02:24.50,Default,,0000,0000,0000,,In this case, since it's\Nopen circuit there'll be
Dialogue: 0,0:02:24.50,0:02:26.76,Default,,0000,0000,0000,,no current flowing through here,
Dialogue: 0,0:02:26.76,0:02:30.70,Default,,0000,0000,0000,,and the voltage V12 will simply equal V,
Dialogue: 0,0:02:30.70,0:02:33.68,Default,,0000,0000,0000,,the open circuit will equal
Dialogue: 0,0:02:33.68,0:02:41.52,Default,,0000,0000,0000,,V sub s. Down here when\Nthe terminals one and two are open,
Dialogue: 0,0:02:41.52,0:02:43.73,Default,,0000,0000,0000,,no current is coming this way.
Dialogue: 0,0:02:43.73,0:02:46.12,Default,,0000,0000,0000,,So in this case, all of\Nthe current from the source is
Dialogue: 0,0:02:46.12,0:02:49.76,Default,,0000,0000,0000,,going through this parallel impedance,
Dialogue: 0,0:02:49.76,0:02:52.43,Default,,0000,0000,0000,,and the voltage that you\Nwould then measure here,
Dialogue: 0,0:02:52.43,0:02:54.92,Default,,0000,0000,0000,,this V open circuit,
Dialogue: 0,0:02:54.92,0:03:03.72,Default,,0000,0000,0000,,would equal just I sub s times\NZ sub s. From this then,
Dialogue: 0,0:03:03.72,0:03:06.70,Default,,0000,0000,0000,,we can write directly what\Nthe relationship needs to be.
Dialogue: 0,0:03:06.70,0:03:11.11,Default,,0000,0000,0000,,In order for these two open-circuit\Nvoltages to be the same,
Dialogue: 0,0:03:11.11,0:03:14.48,Default,,0000,0000,0000,,this V_OC which is V sub s,
Dialogue: 0,0:03:14.48,0:03:17.54,Default,,0000,0000,0000,,must equal this open- circuit voltage here,
Dialogue: 0,0:03:17.54,0:03:24.65,Default,,0000,0000,0000,,I sub s times Z sub s. So in transforming
Dialogue: 0,0:03:24.65,0:03:26.69,Default,,0000,0000,0000,,a current source with
Dialogue: 0,0:03:26.69,0:03:32.16,Default,,0000,0000,0000,,a parallel impedance into\Na voltage source with a series impedance,
Dialogue: 0,0:03:32.16,0:03:35.84,Default,,0000,0000,0000,,the voltage source here\Nwould be equal to I sub
Dialogue: 0,0:03:35.84,0:03:40.41,Default,,0000,0000,0000,,s times Z sub s. Simply rearranging it,
Dialogue: 0,0:03:40.41,0:03:43.47,Default,,0000,0000,0000,,we can come up with\Nan expression for I sub s in
Dialogue: 0,0:03:43.47,0:03:46.95,Default,,0000,0000,0000,,terms of V sub s. That would\Nbe I sub s equals V sub s
Dialogue: 0,0:03:46.95,0:03:55.17,Default,,0000,0000,0000,,over Z sub s. So if we had\Na series voltage source and impedance,
Dialogue: 0,0:03:55.17,0:04:00.42,Default,,0000,0000,0000,,we could replace those with a parallel\Ncurrent source and impedance.
Dialogue: 0,0:04:00.42,0:04:07.78,Default,,0000,0000,0000,,If I sub s here was equal to\Nthe quantity V sub s divided by Z sub s,
Dialogue: 0,0:04:07.78,0:04:10.78,Default,,0000,0000,0000,,we get a little bit better\Nfeel for that by looking
Dialogue: 0,0:04:10.78,0:04:13.84,Default,,0000,0000,0000,,at what is referred to as\Nthe short circuit current.
Dialogue: 0,0:04:13.84,0:04:18.77,Default,,0000,0000,0000,,If you short this out here\Nand call it I short circuit,
Dialogue: 0,0:04:18.77,0:04:24.35,Default,,0000,0000,0000,,we should expect to experience\Nthe same I short circuit,
Dialogue: 0,0:04:24.35,0:04:27.54,Default,,0000,0000,0000,,the same current through this short here.
Dialogue: 0,0:04:27.54,0:04:29.32,Default,,0000,0000,0000,,Well in this circuit here,
Dialogue: 0,0:04:29.32,0:04:33.62,Default,,0000,0000,0000,,I short circuit, in other words\Nzero resistance there,
Dialogue: 0,0:04:33.62,0:04:38.90,Default,,0000,0000,0000,,the current there is just\Ngoing to be V sub s divided by
Dialogue: 0,0:04:38.90,0:04:46.53,Default,,0000,0000,0000,,Z sub s. On the other hand down\Nhere with this being shorted,
Dialogue: 0,0:04:46.53,0:04:50.42,Default,,0000,0000,0000,,it shorts out the impedance and so\Nnone of the current goes through here.
Dialogue: 0,0:04:50.42,0:04:57.26,Default,,0000,0000,0000,,The short-circuit current then would\Nbe simply I sub s or I short circuit
Dialogue: 0,0:04:57.26,0:05:04.48,Default,,0000,0000,0000,,equals I sub s. Here we then see that in\Norder for these two to be equivalent,
Dialogue: 0,0:05:04.48,0:05:11.37,Default,,0000,0000,0000,,I sub s equals V sub s over\NZ sub s as we saw there.