[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.24,Default,,0000,0000,0000,,>> Similar to the concept that\Ncurrent division applies in
Dialogue: 0,0:00:03.24,0:00:06.36,Default,,0000,0000,0000,,exactly the same way or in an analogous\Nway as we've ever to put it in
Dialogue: 0,0:00:06.36,0:00:12.62,Default,,0000,0000,0000,,an analogous way to what we saw when\Nwe had two resistances in parallel.
Dialogue: 0,0:00:12.62,0:00:19.45,Default,,0000,0000,0000,,So we have this current\NI sub S flowing into a node.
Dialogue: 0,0:00:19.55,0:00:26.05,Default,,0000,0000,0000,,Part of that current is going to\Ncome down here in flow through Z_1,
Dialogue: 0,0:00:26.05,0:00:30.77,Default,,0000,0000,0000,,and the other part of the current will\Nflow down into Z_2 and of course,
Dialogue: 0,0:00:30.77,0:00:35.78,Default,,0000,0000,0000,,I_1 plus I_2 must equal I sub S. So we
Dialogue: 0,0:00:35.78,0:00:43.04,Default,,0000,0000,0000,,have I_1 is equal to I sub S times.
Dialogue: 0,0:00:43.04,0:00:45.35,Default,,0000,0000,0000,,So we're talking about the current\Ncoming down here and just as it
Dialogue: 0,0:00:45.35,0:00:49.66,Default,,0000,0000,0000,,was when we had resistances in series,
Dialogue: 0,0:00:49.66,0:00:55.16,Default,,0000,0000,0000,,this current here was proportional\Nto this impedance now.
Dialogue: 0,0:00:55.16,0:00:57.82,Default,,0000,0000,0000,,So the larger this impedance,
Dialogue: 0,0:00:57.82,0:00:59.73,Default,,0000,0000,0000,,the greater the current flowing down here.
Dialogue: 0,0:00:59.73,0:01:05.14,Default,,0000,0000,0000,,You can think of it as the more restricted\Nthis path is for a current to flow,
Dialogue: 0,0:01:05.14,0:01:07.42,Default,,0000,0000,0000,,the more current you'll have over here.
Dialogue: 0,0:01:07.42,0:01:10.84,Default,,0000,0000,0000,,So I_1 is proportional to Z_2,
Dialogue: 0,0:01:10.84,0:01:19.57,Default,,0000,0000,0000,,and it is then I_1 equals I sub S\Ntimes Z_2 over Z_1 plus Z_2.
Dialogue: 0,0:01:19.67,0:01:26.00,Default,,0000,0000,0000,,Similarly, I_2, the current flowing\Nthrough here is going to be proportional
Dialogue: 0,0:01:26.00,0:01:34.15,Default,,0000,0000,0000,,to Z_1 or times I sub S\Ntimes Z_1 over Z_1 plus Z_2,
Dialogue: 0,0:01:34.15,0:01:37.68,Default,,0000,0000,0000,,and again, it's a pretty simple\Nexercise to show that I_1
Dialogue: 0,0:01:37.68,0:01:44.69,Default,,0000,0000,0000,,plus I_2 must equal I sub S. That comes\Njust from Kirchhoff's Current Law.
Dialogue: 0,0:01:44.69,0:01:49.44,Default,,0000,0000,0000,,Again let's just do an example\Nusing I sub S equals that Z_1,
Dialogue: 0,0:01:49.44,0:01:51.94,Default,,0000,0000,0000,,Z_2, the same Z_1 and Z_2\Nwe were using before.
Dialogue: 0,0:01:51.94,0:01:59.06,Default,,0000,0000,0000,,So in this case I_1 is going to\Nequal I sub S which is 2e to
Dialogue: 0,0:01:59.06,0:02:07.68,Default,,0000,0000,0000,,the j25 times Z_2 which is
Dialogue: 0,0:02:07.68,0:02:16.35,Default,,0000,0000,0000,,5 minus j divided by the sum
Dialogue: 0,0:02:16.35,0:02:25.62,Default,,0000,0000,0000,,Z_1 plus Z_2 which is\Nthree plus j2 plus 5 minus j.
Dialogue: 0,0:02:25.62,0:02:28.06,Default,,0000,0000,0000,,When you do the calculations on that,
Dialogue: 0,0:02:28.06,0:02:32.16,Default,,0000,0000,0000,,you get then that I_1 is equal to
Dialogue: 0,0:02:32.16,0:02:41.58,Default,,0000,0000,0000,,1.26e to the j6.57 degrees.
Dialogue: 0,0:02:41.58,0:02:46.22,Default,,0000,0000,0000,,That's I_1 and we can do I_2 right here,
Dialogue: 0,0:02:46.22,0:02:52.62,Default,,0000,0000,0000,,I_2 then is equal to I sub S\Nto e to the j25 times Z_1,
Dialogue: 0,0:02:52.62,0:02:58.47,Default,,0000,0000,0000,,which is 3 plus j2 over Z_1 plus Z_2,
Dialogue: 0,0:02:58.47,0:03:04.28,Default,,0000,0000,0000,,or 3 plus j2 plus 5 minus j.
Dialogue: 0,0:03:04.28,0:03:06.68,Default,,0000,0000,0000,,You did the calculations on that,
Dialogue: 0,0:03:06.68,0:03:09.03,Default,,0000,0000,0000,,and you get that I_2 is equal to
Dialogue: 0,0:03:09.03,0:03:14.51,Default,,0000,0000,0000,,0.894e to
Dialogue: 0,0:03:14.51,0:03:20.22,Default,,0000,0000,0000,,the j51.57.
Dialogue: 0,0:03:20.22,0:03:26.28,Default,,0000,0000,0000,,Again, I'll leave it to you to show\Nthat I_1 plus I_2 is equal to I sub S,
Dialogue: 0,0:03:26.28,0:03:31.93,Default,,0000,0000,0000,,which was 2e to the j25.