[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.14,0:00:06.73,Default,,0000,0000,0000,,Alright, let's formalize our\Napproach to mesh analysis.
Dialogue: 0,0:00:06.73,0:00:10.06,Default,,0000,0000,0000,,When analyzing a circuit using mesh\Nanalysis we first of all identify
Dialogue: 0,0:00:10.06,0:00:11.19,Default,,0000,0000,0000,,the meshes.
Dialogue: 0,0:00:11.19,0:00:15.30,Default,,0000,0000,0000,,Once again, a mesh is a closed loop\Nthat contains no other loops within it.
Dialogue: 0,0:00:16.44,0:00:19.25,Default,,0000,0000,0000,,We'll next assign variable names for\Neach of the mesh currents.
Dialogue: 0,0:00:20.75,0:00:24.30,Default,,0000,0000,0000,,We'll then write KVL equations around\Neach mesh in terms of the mesh current.
Dialogue: 0,0:00:25.62,0:00:30.88,Default,,0000,0000,0000,,And then at that point, we have a system\Nof equations in terms of our mesh currents
Dialogue: 0,0:00:30.88,0:00:34.88,Default,,0000,0000,0000,,that simply need to be solved, and\Nwe've got the problem taken care of.
Dialogue: 0,0:00:35.90,0:00:38.77,Default,,0000,0000,0000,,Let's take a look at this circuit here.
Dialogue: 0,0:00:38.77,0:00:41.13,Default,,0000,0000,0000,,First of all, identify the meshes.
Dialogue: 0,0:00:41.13,0:00:47.11,Default,,0000,0000,0000,,We've got a mesh here on the left,\Nwe've got this upper mash, a lower mesh.
Dialogue: 0,0:00:47.11,0:00:51.72,Default,,0000,0000,0000,,And again, this outer loop is not a mesh\Nbecause in this case it contains three
Dialogue: 0,0:00:51.72,0:00:53.75,Default,,0000,0000,0000,,different meshes within it.
Dialogue: 0,0:00:53.75,0:00:57.87,Default,,0000,0000,0000,,So we identify then or we define three\Ndifferent mesh currents, one for
Dialogue: 0,0:00:57.87,0:00:59.62,Default,,0000,0000,0000,,each of the meshes.
Dialogue: 0,0:00:59.62,0:01:04.88,Default,,0000,0000,0000,,We'll define the current\NIn this mesh to be i1 and
Dialogue: 0,0:01:04.88,0:01:09.42,Default,,0000,0000,0000,,referenced in that direction,\Nthe mesh in the other,
Dialogue: 0,0:01:09.42,0:01:15.50,Default,,0000,0000,0000,,mesh current in this mesh we call i2 and\Nthe mesh current in this mesh we call i3.
Dialogue: 0,0:01:16.90,0:01:20.68,Default,,0000,0000,0000,,Lets go ahead now then and write the three
Dialogue: 0,0:01:20.68,0:01:25.70,Default,,0000,0000,0000,,Mesh equations in terms of I 1 and\NI 2 and I 3 starting right here.
Dialogue: 0,0:01:27.19,0:01:31.27,Default,,0000,0000,0000,,Going up this way we cross the voltage\Nsource going from minus to plus
Dialogue: 0,0:01:31.27,0:01:35.89,Default,,0000,0000,0000,,therefore it's a voltage increase and\Nagain that would be a negative V 0.
Dialogue: 0,0:01:35.89,0:01:41.73,Default,,0000,0000,0000,,Plus the votage drop across\NR1 is just R1 times I1.
Dialogue: 0,0:01:43.13,0:01:46.33,Default,,0000,0000,0000,,Now coming down across R2,\Nwe need to be carefully.
Dialogue: 0,0:01:46.33,0:01:51.20,Default,,0000,0000,0000,,The current through R2
Dialogue: 0,0:01:51.20,0:01:57.07,Default,,0000,0000,0000,,involves two different mis currents\Nbecause we are going down at this point
Dialogue: 0,0:01:57.07,0:02:02.01,Default,,0000,0000,0000,,The current through here is gonna be the\Nmesh current reference down which is I 1,
Dialogue: 0,0:02:02.01,0:02:06.19,Default,,0000,0000,0000,,minus I 2, which is referenced\Nin the opposite direction.
Dialogue: 0,0:02:06.19,0:02:13.82,Default,,0000,0000,0000,,So we'll have then plus\NR 2 times I 1 minus I 2.
Dialogue: 0,0:02:16.68,0:02:19.27,Default,,0000,0000,0000,,Now continuing on down, across R5.
Dialogue: 0,0:02:19.27,0:02:26.65,Default,,0000,0000,0000,,The current flowing through\NR5 is going to be I1- I3.
Dialogue: 0,0:02:32.73,0:02:35.10,Default,,0000,0000,0000,,And those terms must then add to 0.
Dialogue: 0,0:02:36.61,0:02:39.36,Default,,0000,0000,0000,,Let's take a look at the top mesh.
Dialogue: 0,0:02:39.36,0:02:42.76,Default,,0000,0000,0000,,Starting right here and
Dialogue: 0,0:02:42.76,0:02:48.54,Default,,0000,0000,0000,,going up we've got R2 times the current
Dialogue: 0,0:02:48.54,0:02:53.48,Default,,0000,0000,0000,,flowing up which is I2 minus I1.
Dialogue: 0,0:02:53.48,0:02:58.38,Default,,0000,0000,0000,,And again let us just point\Nout that the current going up
Dialogue: 0,0:02:58.38,0:03:03.61,Default,,0000,0000,0000,,I2 minus I1 In this equation\Nis the opposite current that
Dialogue: 0,0:03:03.61,0:03:09.48,Default,,0000,0000,0000,,was flowing down which was I1- I2 and\Nthis equation.
Dialogue: 0,0:03:09.48,0:03:13.00,Default,,0000,0000,0000,,All right continuing on\Naround we have in plus
Dialogue: 0,0:03:14.76,0:03:18.10,Default,,0000,0000,0000,,R3 times the current\Nthrough R3 is simply I2.
Dialogue: 0,0:03:20.02,0:03:24.93,Default,,0000,0000,0000,,Coming back to the left through R4\Nwe'll have plus R4 times the current
Dialogue: 0,0:03:24.93,0:03:29.88,Default,,0000,0000,0000,,flowing in R4, which
Dialogue: 0,0:03:29.88,0:03:35.75,Default,,0000,0000,0000,,is I2- I3.
Dialogue: 0,0:03:40.79,0:03:44.67,Default,,0000,0000,0000,,That brings us back to where we started so\Nthe sum of those terms must equal zero.
Dialogue: 0,0:03:45.67,0:03:49.54,Default,,0000,0000,0000,,And finally we do a KVL around this bottom
Dialogue: 0,0:03:49.54,0:03:54.04,Default,,0000,0000,0000,,mesh starting here and\Nwe'll have R five times
Dialogue: 0,0:03:54.04,0:03:58.54,Default,,0000,0000,0000,,the current flowing through R five in the\Ndirection we're going which is I three.
Dialogue: 0,0:03:58.54,0:03:59.97,Default,,0000,0000,0000,,Minus I1
Dialogue: 0,0:04:05.48,0:04:10.52,Default,,0000,0000,0000,,plus coming across here, plus R4 times
Dialogue: 0,0:04:10.52,0:04:15.72,Default,,0000,0000,0000,,the current flowing left to right in R4.
Dialogue: 0,0:04:15.72,0:04:21.40,Default,,0000,0000,0000,,In terms of the mesh\Ncurrents is I3 minus i2 and
Dialogue: 0,0:04:23.10,0:04:28.64,Default,,0000,0000,0000,,than finally the current coming down\Nhere through that r6 will be r6 times i3
Dialogue: 0,0:04:28.64,0:04:33.73,Default,,0000,0000,0000,,and than some of those\Ncurrents equal zero.
Dialogue: 0,0:04:35.99,0:04:37.33,Default,,0000,0000,0000,,Up here, lets just go ahead and
Dialogue: 0,0:04:37.33,0:04:42.06,Default,,0000,0000,0000,,complete this by factoring out the mesh\Ncurrents and combining like terms.
Dialogue: 0,0:04:42.06,0:04:47.14,Default,,0000,0000,0000,,We have, for the top one,\Nthe top equation we've got I1 times R1.
Dialogue: 0,0:04:47.14,0:04:48.61,Default,,0000,0000,0000,,Let's see what we've got.
Dialogue: 0,0:04:48.61,0:04:50.80,Default,,0000,0000,0000,,R1 there, there and there.
Dialogue: 0,0:04:50.80,0:04:53.13,Default,,0000,0000,0000,,So, we've R1 plus R2 plus R5.
Dialogue: 0,0:04:57.51,0:05:02.60,Default,,0000,0000,0000,,+ I2 times, we have one I2 term there,
Dialogue: 0,0:05:02.60,0:05:05.37,Default,,0000,0000,0000,,it's got a negative.
Dialogue: 0,0:05:08.14,0:05:15.93,Default,,0000,0000,0000,,R2 + I3 We've got one I3 term here\Nwith a negative sign in front of it.
Dialogue: 0,0:05:15.93,0:05:20.22,Default,,0000,0000,0000,,So that would be I + I3\Ntimes a negative R5.
Dialogue: 0,0:05:20.22,0:05:24.88,Default,,0000,0000,0000,,And the sum of those then equals,\Nwe've got the negative V0 that we
Dialogue: 0,0:05:24.88,0:05:27.76,Default,,0000,0000,0000,,need to bring over to\Nthe other side as a positive.
Dialogue: 0,0:05:29.22,0:05:34.26,Default,,0000,0000,0000,,V 0 combining like terms in the second\Nequation we factor out the I 2 I'm
Dialogue: 0,0:05:34.26,0:05:39.19,Default,,0000,0000,0000,,sorry the I 1 here and I've got one
Dialogue: 0,0:05:40.86,0:05:46.66,Default,,0000,0000,0000,,I 1 term, it's got a negative on it so\Nit'd be a negative
Dialogue: 0,0:05:46.66,0:05:51.38,Default,,0000,0000,0000,,R 2 Plus I2 times.
Dialogue: 0,0:05:51.38,0:05:54.66,Default,,0000,0000,0000,,You've got I2 here, here, and here.
Dialogue: 0,0:05:54.66,0:05:59.54,Default,,0000,0000,0000,,All positives will be R2 plus R3 plus R4.
Dialogue: 0,0:05:59.54,0:06:06.68,Default,,0000,0000,0000,,Plus R3 plus R4 and
Dialogue: 0,0:06:06.68,0:06:11.97,Default,,0000,0000,0000,,then our I3 turns There is only one.
Dialogue: 0,0:06:13.72,0:06:15.84,Default,,0000,0000,0000,,It's got a negative, so\Nit'll be a negative R4.
Dialogue: 0,0:06:18.69,0:06:20.36,Default,,0000,0000,0000,,And the sum of those\Nterms have to equal 0.
Dialogue: 0,0:06:20.36,0:06:26.28,Default,,0000,0000,0000,,And finally, the bottom equation here,\Nfactoring out the I1s to begin with.
Dialogue: 0,0:06:26.28,0:06:28.01,Default,,0000,0000,0000,,I've got an I1 term here.
Dialogue: 0,0:06:29.40,0:06:30.68,Default,,0000,0000,0000,,Times what is that?
Dialogue: 0,0:06:30.68,0:06:32.06,Default,,0000,0000,0000,,That's R5 isn't it?
Dialogue: 0,0:06:34.55,0:06:37.66,Default,,0000,0000,0000,,So I1's got a negative R5.
Dialogue: 0,0:06:41.02,0:06:41.55,Default,,0000,0000,0000,,Plus I2.
Dialogue: 0,0:06:41.55,0:06:45.92,Default,,0000,0000,0000,,once again there's only one I2\N[INAUDIBLE] has a negative R4.
Dialogue: 0,0:06:48.35,0:06:49.14,Default,,0000,0000,0000,,Plus I3.
Dialogue: 0,0:06:49.14,0:06:53.27,Default,,0000,0000,0000,,And there are three I3 terms,
Dialogue: 0,0:06:53.27,0:07:01.31,Default,,0000,0000,0000,,I got R4 plus R5 plus R6,
Dialogue: 0,0:07:01.31,0:07:06.82,Default,,0000,0000,0000,,R4 + R5 + R6.
Dialogue: 0,0:07:06.82,0:07:10.06,Default,,0000,0000,0000,,And the sum of those has to equal 0.
Dialogue: 0,0:07:10.06,0:07:15.20,Default,,0000,0000,0000,,Plug it in, well, of course, with\Nthe values of the resistors and the V0,
Dialogue: 0,0:07:15.20,0:07:20.95,Default,,0000,0000,0000,,plug it in to your matrix solver or\Nyour solve button on your calculator,
Dialogue: 0,0:07:20.95,0:07:24.78,Default,,0000,0000,0000,,and you've got everything you need\Nto calculate those mesh currents.
Dialogue: 0,0:07:24.78,0:07:27.79,Default,,0000,0000,0000,,Once you know the mesh currents you\Ncan calculate any branch voltage or
Dialogue: 0,0:07:27.79,0:07:30.29,Default,,0000,0000,0000,,branch current that you\Nmight be interested in.