0:00:00.000,0:00:03.240
>> Similar to the concept that[br]current division applies in

0:00:03.240,0:00:06.360
exactly the same way or in an analogous[br]way as we've ever to put it in

0:00:06.360,0:00:12.625
an analogous way to what we saw when[br]we had two resistances in parallel.

0:00:12.625,0:00:19.450
So we have this current[br]I sub S flowing into a node.

0:00:19.550,0:00:26.050
Part of that current is going to[br]come down here in flow through Z_1,

0:00:26.050,0:00:30.770
and the other part of the current will[br]flow down into Z_2 and of course,

0:00:30.770,0:00:35.780
I_1 plus I_2 must equal I sub S. So we

0:00:35.780,0:00:43.035
have I_1 is equal to I sub S times.

0:00:43.035,0:00:45.350
So we're talking about the current[br]coming down here and just as it

0:00:45.350,0:00:49.655
was when we had resistances in series,

0:00:49.655,0:00:55.160
this current here was proportional[br]to this impedance now.

0:00:55.160,0:00:57.820
So the larger this impedance,

0:00:57.820,0:00:59.730
the greater the current flowing down here.

0:00:59.730,0:01:05.135
You can think of it as the more restricted[br]this path is for a current to flow,

0:01:05.135,0:01:07.415
the more current you'll have over here.

0:01:07.415,0:01:10.845
So I_1 is proportional to Z_2,

0:01:10.845,0:01:19.570
and it is then I_1 equals I sub S[br]times Z_2 over Z_1 plus Z_2.

0:01:19.670,0:01:26.000
Similarly, I_2, the current flowing[br]through here is going to be proportional

0:01:26.000,0:01:34.150
to Z_1 or times I sub S[br]times Z_1 over Z_1 plus Z_2,

0:01:34.150,0:01:37.685
and again, it's a pretty simple[br]exercise to show that I_1

0:01:37.685,0:01:44.690
plus I_2 must equal I sub S. That comes[br]just from Kirchhoff's Current Law.

0:01:44.690,0:01:49.440
Again let's just do an example[br]using I sub S equals that Z_1,

0:01:49.440,0:01:51.945
Z_2, the same Z_1 and Z_2[br]we were using before.

0:01:51.945,0:01:59.060
So in this case I_1 is going to[br]equal I sub S which is 2e to

0:01:59.060,0:02:07.685
the j25 times Z_2 which is

0:02:07.685,0:02:16.350
5 minus j divided by the sum

0:02:16.350,0:02:25.620
Z_1 plus Z_2 which is[br]three plus j2 plus 5 minus j.

0:02:25.620,0:02:28.060
When you do the calculations on that,

0:02:28.060,0:02:32.160
you get then that I_1 is equal to

0:02:32.160,0:02:41.580
1.26e to the j6.57 degrees.

0:02:41.580,0:02:46.215
That's I_1 and we can do I_2 right here,

0:02:46.215,0:02:52.620
I_2 then is equal to I sub S[br]to e to the j25 times Z_1,

0:02:52.620,0:02:58.470
which is 3 plus j2 over Z_1 plus Z_2,

0:02:58.470,0:03:04.275
or 3 plus j2 plus 5 minus j.

0:03:04.275,0:03:06.675
You did the calculations on that,

0:03:06.675,0:03:09.030
and you get that I_2 is equal to

0:03:09.030,0:03:14.510
0.894e to

0:03:14.510,0:03:20.220
the j51.57.

0:03:20.220,0:03:26.280
Again, I'll leave it to you to show[br]that I_1 plus I_2 is equal to I sub S,

0:03:26.280,0:03:31.930
which was 2e to the j25.