[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:04.56,Default,,0000,0000,0000,,In this video we're gonna take a look at\Nusing node analysis techniques to analyze
Dialogue: 0,0:00:04.56,0:00:06.95,Default,,0000,0000,0000,,a circuit that's got a dependent source.
Dialogue: 0,0:00:06.95,0:00:11.90,Default,,0000,0000,0000,,You'll notice right off the bat that\Nwe got a dependent current source
Dialogue: 0,0:00:11.90,0:00:13.41,Default,,0000,0000,0000,,here in this branch.
Dialogue: 0,0:00:13.41,0:00:18.19,Default,,0000,0000,0000,,This dependent current source,\Nthe amount of current that this current is
Dialogue: 0,0:00:18.19,0:00:23.04,Default,,0000,0000,0000,,producing depends upon the current i\Nflowing through the 6 ohm resistor and
Dialogue: 0,0:00:23.04,0:00:26.24,Default,,0000,0000,0000,,this current source, then,\Nis two times that I.
Dialogue: 0,0:00:26.24,0:00:30.23,Default,,0000,0000,0000,,We're gonna take that into account as we\Ngo through and define our node voltages
Dialogue: 0,0:00:30.23,0:00:33.87,Default,,0000,0000,0000,,and we'll come up with an expression for\NI in terms of our node voltages.
Dialogue: 0,0:00:33.87,0:00:36.03,Default,,0000,0000,0000,,So let's go ahead and get started.
Dialogue: 0,0:00:36.03,0:00:37.54,Default,,0000,0000,0000,,We've got three critical nodes again.
Dialogue: 0,0:00:37.54,0:00:40.11,Default,,0000,0000,0000,,One here, one here, and\None along the bottom.
Dialogue: 0,0:00:40.11,0:00:43.70,Default,,0000,0000,0000,,Once again, we'll go ahead and\Ncall this our reference node,
Dialogue: 0,0:00:43.70,0:00:45.41,Default,,0000,0000,0000,,where we've got v equals 0.
Dialogue: 0,0:00:45.41,0:00:50.71,Default,,0000,0000,0000,,And once again, we've got a voltage\Nsource tied to the reference,
Dialogue: 0,0:00:50.71,0:00:56.94,Default,,0000,0000,0000,,so we know the voltage here at this point\Nof our circuit is equal to 5.3 volts.
Dialogue: 0,0:00:56.94,0:01:03.75,Default,,0000,0000,0000,,We'll define this node here to be V1,\Nthis node here to be V2.
Dialogue: 0,0:01:03.75,0:01:08.58,Default,,0000,0000,0000,,And with those two defined\Nvoltages now we can express i,
Dialogue: 0,0:01:08.58,0:01:11.70,Default,,0000,0000,0000,,the current i In terms of V1 and V2.
Dialogue: 0,0:01:11.70,0:01:16.68,Default,,0000,0000,0000,,In fact I is equal to V1\Nminus V2 divided by 6 ohms,
Dialogue: 0,0:01:16.68,0:01:20.88,Default,,0000,0000,0000,,it's just the voltage\Nhere on the left minus
Dialogue: 0,0:01:20.88,0:01:25.09,Default,,0000,0000,0000,,the voltage on the right\Ndivided by 6 ohms.
Dialogue: 0,0:01:28.24,0:01:31.04,Default,,0000,0000,0000,,When we're all done with this analysis,
Dialogue: 0,0:01:31.04,0:01:35.13,Default,,0000,0000,0000,,we're going to use that expression\Nto calculate I let's say
Dialogue: 0,0:01:35.13,0:01:39.55,Default,,0000,0000,0000,,to calculate the power being\Nproduced by this dependent source.
Dialogue: 0,0:01:39.55,0:01:41.82,Default,,0000,0000,0000,,With those definitions, let's go ahead and
Dialogue: 0,0:01:41.82,0:01:44.10,Default,,0000,0000,0000,,write the node equations\Nat these two nodes.
Dialogue: 0,0:01:44.10,0:01:46.89,Default,,0000,0000,0000,,First one here on the left\Nthe current leaving.
Dialogue: 0,0:01:46.89,0:01:51.07,Default,,0000,0000,0000,,The first node here going\Nto the left is going to be,
Dialogue: 0,0:01:51.07,0:01:55.73,Default,,0000,0000,0000,,V1-5.3 divided by 4 ohms\N+ the current coming down
Dialogue: 0,0:01:55.73,0:02:00.59,Default,,0000,0000,0000,,here through the 3 ohm resistor\Nis going to be V1 divided by
Dialogue: 0,0:02:00.59,0:02:05.08,Default,,0000,0000,0000,,3 + the current leaving this\Nnode going to the right.
Dialogue: 0,0:02:05.08,0:02:09.40,Default,,0000,0000,0000,,Well notice that that's that\Ncurrent I has been defined for us.
Dialogue: 0,0:02:09.40,0:02:13.98,Default,,0000,0000,0000,,We don't want to use I we want to use or\Nwe want an expression for
Dialogue: 0,0:02:13.98,0:02:18.31,Default,,0000,0000,0000,,that current in terms of\Nthe node voltages V1 and V2, and
Dialogue: 0,0:02:18.31,0:02:23.71,Default,,0000,0000,0000,,we've already expressed that I over\Nhere as V1 minus V2 divided by 6.
Dialogue: 0,0:02:23.71,0:02:28.90,Default,,0000,0000,0000,,So plus V1-V2 divided by 6.
Dialogue: 0,0:02:28.90,0:02:32.17,Default,,0000,0000,0000,,The sum of those three\Ncurrents has to equal 0.
Dialogue: 0,0:02:32.17,0:02:35.69,Default,,0000,0000,0000,,Now let's write the node\Nequation of the V2 node.
Dialogue: 0,0:02:35.69,0:02:40.74,Default,,0000,0000,0000,,Current going to the left is going to
Dialogue: 0,0:02:40.74,0:02:48.32,Default,,0000,0000,0000,,be V2-V1 divided by 6\N+ V2-0 divided by 12.
Dialogue: 0,0:02:49.98,0:02:53.42,Default,,0000,0000,0000,,Minus, okay, now let's be careful.
Dialogue: 0,0:02:53.42,0:02:59.58,Default,,0000,0000,0000,,Minus two times I, it's minus because\Nit's referenced into the node.
Dialogue: 0,0:02:59.58,0:03:05.08,Default,,0000,0000,0000,,Two times I is this dependent source,\Nbut I don't want to put I in here.
Dialogue: 0,0:03:05.08,0:03:08.56,Default,,0000,0000,0000,,We want to write everything in\Nterms of our node variables or
Dialogue: 0,0:03:08.56,0:03:10.73,Default,,0000,0000,0000,,node voltage variables V1 and V2.
Dialogue: 0,0:03:10.73,0:03:16.75,Default,,0000,0000,0000,,So I've got i is equal to two,\Nor v1 minus v2 divided by 6.
Dialogue: 0,0:03:16.75,0:03:21.97,Default,,0000,0000,0000,,This current here is two times I so\Nit's going
Dialogue: 0,0:03:21.97,0:03:27.05,Default,,0000,0000,0000,,to be -2 times v1 minus v2 divided by 6,
Dialogue: 0,0:03:27.05,0:03:32.01,Default,,0000,0000,0000,,the sum of those three currents equals 0.
Dialogue: 0,0:03:32.01,0:03:35.81,Default,,0000,0000,0000,,I suggest that you stop the video right\Nnow and just take a look at that,
Dialogue: 0,0:03:35.81,0:03:38.15,Default,,0000,0000,0000,,there's a couple of things going on here.
Dialogue: 0,0:03:38.15,0:03:41.61,Default,,0000,0000,0000,,The fact that it's going into\Nthe node gives us the minus sign.
Dialogue: 0,0:03:41.61,0:03:43.50,Default,,0000,0000,0000,,It's gonna be minus\Nthe current flowing in.
Dialogue: 0,0:03:43.50,0:03:47.70,Default,,0000,0000,0000,,Well, the current flowing in is 2 times or
Dialogue: 0,0:03:47.70,0:03:51.33,Default,,0000,0000,0000,,has a value of 2 times whatever I is.
Dialogue: 0,0:03:51.33,0:03:55.36,Default,,0000,0000,0000,,We defined I as V1- V2 divided by 6.
Dialogue: 0,0:03:55.36,0:04:02.76,Default,,0000,0000,0000,,So we have, then,\N-2 times V1- V2 divided by 6.
Dialogue: 0,0:04:02.76,0:04:06.94,Default,,0000,0000,0000,,Alrighty, now that you've taken a moment\Nto make sure you understand what we did
Dialogue: 0,0:04:06.94,0:04:09.10,Default,,0000,0000,0000,,there with the signs, let's go ahead and
Dialogue: 0,0:04:09.10,0:04:13.18,Default,,0000,0000,0000,,solve this system of two equations with\Ntwo unknowns by combining like terms.
Dialogue: 0,0:04:13.18,0:04:19.74,Default,,0000,0000,0000,,For the first equation we've got
Dialogue: 0,0:04:19.74,0:04:27.01,Default,,0000,0000,0000,,V1 times one-fourth + one-third
Dialogue: 0,0:04:27.01,0:04:32.65,Default,,0000,0000,0000,,+ one- sixth + V2 times.
Dialogue: 0,0:04:32.65,0:04:38.32,Default,,0000,0000,0000,,This is just one V2 term that's got\Na negative one- sixth with it is
Dialogue: 0,0:04:38.32,0:04:45.21,Default,,0000,0000,0000,,equal to negative 5 divided by 4 take it\Nto the other side as I'm sorry negative.
Dialogue: 0,0:04:45.21,0:04:49.30,Default,,0000,0000,0000,,Let's see, it's -5.3 divided by 4,
Dialogue: 0,0:04:49.30,0:04:53.95,Default,,0000,0000,0000,,take it to the other side\Nis a +5.3 divided by 4
Dialogue: 0,0:04:53.95,0:04:58.84,Default,,0000,0000,0000,,will write it like that for\Nnow 5.3 divided by 4.
Dialogue: 0,0:04:58.84,0:05:00.55,Default,,0000,0000,0000,,Alrighty, the second equation and
Dialogue: 0,0:05:00.55,0:05:04.20,Default,,0000,0000,0000,,here we're going to need to be careful\Nbecause we've got this stuff going on
Dialogue: 0,0:05:04.20,0:05:07.48,Default,,0000,0000,0000,,there with the last term but\Nonce again factoring out the V1 terms.
Dialogue: 0,0:05:07.48,0:05:12.56,Default,,0000,0000,0000,,Here I've got a V1 term and I've got\Na V1 term here, let's be careful there.
Dialogue: 0,0:05:12.56,0:05:16.10,Default,,0000,0000,0000,,The first one is negative one- sixth.
Dialogue: 0,0:05:16.10,0:05:18.78,Default,,0000,0000,0000,,But what do I actually have over here?
Dialogue: 0,0:05:18.78,0:05:24.46,Default,,0000,0000,0000,,I've got -2 times V1 divided by 6.
Dialogue: 0,0:05:24.46,0:05:28.76,Default,,0000,0000,0000,,So that's negative -2 over 6,\Nthat's negative one third V1.
Dialogue: 0,0:05:28.76,0:05:33.50,Default,,0000,0000,0000,,Factor out the V1, and that leaves me
Dialogue: 0,0:05:33.50,0:05:37.94,Default,,0000,0000,0000,,with a negative one-third there.
Dialogue: 0,0:05:37.94,0:05:42.86,Default,,0000,0000,0000,,Alrighty, now for\Nthe V2 terms, + V2 times,
Dialogue: 0,0:05:42.86,0:05:49.94,Default,,0000,0000,0000,,I've got a V2 over 6, factoring\Nout the V2 leaves me a one-sixth.
Dialogue: 0,0:05:49.94,0:05:54.33,Default,,0000,0000,0000,,I've got a V2 over 12, so + one-twelfth.
Dialogue: 0,0:05:54.33,0:05:55.97,Default,,0000,0000,0000,,Now once again, slow down here.
Dialogue: 0,0:05:55.97,0:05:58.34,Default,,0000,0000,0000,,You've got signs and\Nsigns like red flags waving.
Dialogue: 0,0:05:58.34,0:06:02.02,Default,,0000,0000,0000,,That means slow down, you've got\Nan opportunity to make a sign error and
Dialogue: 0,0:06:02.02,0:06:03.48,Default,,0000,0000,0000,,we don't like sign errors.
Dialogue: 0,0:06:03.48,0:06:07.47,Default,,0000,0000,0000,,We've got -2 times a -V2 over 6.
Dialogue: 0,0:06:07.47,0:06:12.29,Default,,0000,0000,0000,,Negative times a negative\Nis a positive to V2 over 6,
Dialogue: 0,0:06:12.29,0:06:16.58,Default,,0000,0000,0000,,so that's gonna be positive\Nfactor out the V2,
Dialogue: 0,0:06:16.58,0:06:23.73,Default,,0000,0000,0000,,I've got 6 that's one-third, and\Nthe sum of those three currents equals 0.
Dialogue: 0,0:06:23.73,0:06:26.53,Default,,0000,0000,0000,,Once again, I'd encourage you to\Nstop the video at this point and
Dialogue: 0,0:06:26.53,0:06:29.19,Default,,0000,0000,0000,,just make sure that you understand\Nwhat we did with the signs.
Dialogue: 0,0:06:29.19,0:06:36.77,Default,,0000,0000,0000,,Alrighty, let's just Be careful here\Nthat we keep our equations separate,
Dialogue: 0,0:06:36.77,0:06:41.80,Default,,0000,0000,0000,,and now let's go ahead and\Ncombine the fractions.
Dialogue: 0,0:06:41.80,0:06:46.73,Default,,0000,0000,0000,,We've got here then for\Nthe first equation we have v1 times
Dialogue: 0,0:06:46.73,0:06:52.16,Default,,0000,0000,0000,,one-fourth plus one-third plus\None-sixth is three-forth.
Dialogue: 0,0:06:55.36,0:07:01.52,Default,,0000,0000,0000,,Plus V2 time negative one-sixth
Dialogue: 0,0:07:01.52,0:07:08.53,Default,,0000,0000,0000,,= 5.3 divided by 4 is 1.325.
Dialogue: 0,0:07:08.53,0:07:13.50,Default,,0000,0000,0000,,And on the second equation\Nwe have V1 times negative
Dialogue: 0,0:07:13.50,0:07:18.81,Default,,0000,0000,0000,,one-sixth minus one-third\Nis a negative one-half.
Dialogue: 0,0:07:21.30,0:07:26.35,Default,,0000,0000,0000,,Plus V2 times one-sixth + one-twelfths
Dialogue: 0,0:07:26.35,0:07:33.86,Default,,0000,0000,0000,,+ one-third is seven-twelfths and\Nit's positive equals 0.
Dialogue: 0,0:07:35.08,0:07:39.69,Default,,0000,0000,0000,,So we've got our two equations there.
Dialogue: 0,0:07:39.69,0:07:41.70,Default,,0000,0000,0000,,Once again,\Nplug that into your matrix solver,
Dialogue: 0,0:07:41.70,0:07:44.92,Default,,0000,0000,0000,,use the solve button on your calculator or\Nyou can use MATLAB for that matter.
Dialogue: 0,0:07:44.92,0:07:49.45,Default,,0000,0000,0000,,And when you do, you'll get
Dialogue: 0,0:07:49.45,0:07:54.56,Default,,0000,0000,0000,,that V1 equals 2.1824,
Dialogue: 0,0:07:54.56,0:08:01.57,Default,,0000,0000,0000,,2.1824 and V2 is equal to 1.87.
Dialogue: 0,0:08:01.57,0:08:06.55,Default,,0000,0000,0000,,Now what can we do with V1 and\NV2 while we can do anything we need to do.
Dialogue: 0,0:08:06.55,0:08:10.93,Default,,0000,0000,0000,,Just for example in this one, why do\Nwe calculate the power of this being
Dialogue: 0,0:08:10.93,0:08:13.42,Default,,0000,0000,0000,,generated by this dependency source and
Dialogue: 0,0:08:13.42,0:08:18.18,Default,,0000,0000,0000,,let's be careful here because we've\Ngot issues with reference direction.
Dialogue: 0,0:08:18.18,0:08:23.76,Default,,0000,0000,0000,,There is a dependence\Nsource it has a value
Dialogue: 0,0:08:23.76,0:08:28.54,Default,,0000,0000,0000,,of 2 times I, reference going up.
Dialogue: 0,0:08:28.54,0:08:34.78,Default,,0000,0000,0000,,And what is the voltage across that power\Nsupply, well is the reference plus to
Dialogue: 0,0:08:34.78,0:08:41.03,Default,,0000,0000,0000,,minus V2 that power supply that dependent\Ncurrent source has V2 on the top and
Dialogue: 0,0:08:41.03,0:08:47.39,Default,,0000,0000,0000,,it's tied on the bottom to our reference\Nso the voltage across that is just V2.
Dialogue: 0,0:08:47.39,0:08:53.04,Default,,0000,0000,0000,,Now we know that power\Nis equal to I times V.
Dialogue: 0,0:08:55.07,0:09:00.37,Default,,0000,0000,0000,,And we also know that we got to be\Ncareful about the sign in front of this.
Dialogue: 0,0:09:00.37,0:09:04.84,Default,,0000,0000,0000,,Our passive sign convention says that\Nif current is referenced going from
Dialogue: 0,0:09:04.84,0:09:09.02,Default,,0000,0000,0000,,the positive to the negative terminal,\Nit will be a positive power.
Dialogue: 0,0:09:09.02,0:09:12.76,Default,,0000,0000,0000,,That's not what we have here, in this\Ncase, we have the current going up,
Dialogue: 0,0:09:12.76,0:09:16.35,Default,,0000,0000,0000,,referenced into the negative terminal and\Nout the positive terminal.
Dialogue: 0,0:09:16.35,0:09:19.63,Default,,0000,0000,0000,,So that means that we\Nneed a minus sign there.
Dialogue: 0,0:09:19.63,0:09:21.49,Default,,0000,0000,0000,,Now, what is I?
Dialogue: 0,0:09:21.49,0:09:25.68,Default,,0000,0000,0000,,Well, we've got I up here,\NI is V1- V2 divided by 6.
Dialogue: 0,0:09:25.68,0:09:27.96,Default,,0000,0000,0000,,So let's go ahead and calculate that.
Dialogue: 0,0:09:27.96,0:09:35.38,Default,,0000,0000,0000,,V1 was 2.1824 minus V2.
Dialogue: 0,0:09:35.38,0:09:40.42,Default,,0000,0000,0000,,Which was 1.87-1.87,
Dialogue: 0,0:09:40.42,0:09:45.65,Default,,0000,0000,0000,,and the whole thing divided by 6.
Dialogue: 0,0:09:45.65,0:09:50.11,Default,,0000,0000,0000,,That gives us a value for
Dialogue: 0,0:09:50.11,0:09:54.80,Default,,0000,0000,0000,,I of 0.052 amps, or
Dialogue: 0,0:09:54.80,0:10:02.17,Default,,0000,0000,0000,,52 milliamps, so 0.052 amps.
Dialogue: 0,0:10:02.17,0:10:08.67,Default,,0000,0000,0000,,Now this current source right\Nhere is equal to if I sub x,
Dialogue: 0,0:10:08.67,0:10:14.76,Default,,0000,0000,0000,,the current that it generates\Nis equal to 2 times I,
Dialogue: 0,0:10:14.76,0:10:18.10,Default,,0000,0000,0000,,we now know I is 0.052.
Dialogue: 0,0:10:18.10,0:10:22.51,Default,,0000,0000,0000,,So that current source is producing
Dialogue: 0,0:10:22.51,0:10:27.08,Default,,0000,0000,0000,,2 times .052 or .104 amps.
Dialogue: 0,0:10:27.08,0:10:31.66,Default,,0000,0000,0000,,That's the current that we need\Ndown here to calculate the power.
Dialogue: 0,0:10:31.66,0:10:38.57,Default,,0000,0000,0000,,This current source is\Nproducing 0.104 amps going up.
Dialogue: 0,0:10:38.57,0:10:45.32,Default,,0000,0000,0000,,So the power down here is going to\Nbe equal to negative I is 0.104.
Dialogue: 0,0:10:48.76,0:10:50.09,Default,,0000,0000,0000,,Times V, which V did we say it was?
Dialogue: 0,0:10:50.09,0:10:53.16,Default,,0000,0000,0000,,It was V2.
Dialogue: 0,0:10:53.16,0:10:59.28,Default,,0000,0000,0000,,So times V2, which is 1.87 volts,
Dialogue: 0,0:10:59.28,0:11:05.77,Default,,0000,0000,0000,,and when you multiple those two together,
Dialogue: 0,0:11:05.77,0:11:11.54,Default,,0000,0000,0000,,you get a negative 0.194 watts.
Dialogue: 0,0:11:11.54,0:11:14.47,Default,,0000,0000,0000,,Negative, what does the negative\Nsign mean on power?
Dialogue: 0,0:11:14.47,0:11:17.20,Default,,0000,0000,0000,,It means that it's producing energy,
Dialogue: 0,0:11:17.20,0:11:20.92,Default,,0000,0000,0000,,it's the source is putting\Nenergy into the circuit.