[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.13,0:00:03.72,Default,,0000,0000,0000,,>> Closely related to
Dialogue: 0,0:00:03.72,0:00:08.13,Default,,0000,0000,0000,,the series combination of two impedances\Nis concept of voltage division.
Dialogue: 0,0:00:08.13,0:00:12.20,Default,,0000,0000,0000,,We saw voltage division back when we were\Ntalking about resistances in series,
Dialogue: 0,0:00:12.20,0:00:15.40,Default,,0000,0000,0000,,and it probably shouldn't surprise\Nanybody when we see that,
Dialogue: 0,0:00:15.40,0:00:19.37,Default,,0000,0000,0000,,just that the voltage\Ndivision with impedances in
Dialogue: 0,0:00:19.37,0:00:22.67,Default,,0000,0000,0000,,the sinusoidal steady state\Nare of the same type of
Dialogue: 0,0:00:22.67,0:00:26.04,Default,,0000,0000,0000,,calculation as they were when we were\Ndealing with resistances in series.
Dialogue: 0,0:00:26.04,0:00:28.61,Default,,0000,0000,0000,,The only difference, again, is\Nthat we are using complex numbers.
Dialogue: 0,0:00:28.61,0:00:34.28,Default,,0000,0000,0000,,So, for example, we have then V1 is equal
Dialogue: 0,0:00:34.28,0:00:43.03,Default,,0000,0000,0000,,to Vs times Z1 over Z1 plus Z2,
Dialogue: 0,0:00:43.03,0:00:46.42,Default,,0000,0000,0000,,and that would be the voltage\Nacross this impedance,
Dialogue: 0,0:00:46.42,0:00:49.25,Default,,0000,0000,0000,,and V2 is equal to
Dialogue: 0,0:00:49.25,0:00:57.99,Default,,0000,0000,0000,,Vs times Z2 over Z1 plus Z2.
Dialogue: 0,0:00:58.24,0:01:05.36,Default,,0000,0000,0000,,Of course, it's pretty easy to show\Nthat combining V1 plus V2 equals Vs.
Dialogue: 0,0:01:05.36,0:01:09.36,Default,,0000,0000,0000,,So, what we're saying is that you've\Ngot a total of Vs dropped across there,
Dialogue: 0,0:01:09.36,0:01:15.99,Default,,0000,0000,0000,,Z1 over Z1 plus Z2 times Vs is V1,
Dialogue: 0,0:01:15.99,0:01:18.56,Default,,0000,0000,0000,,or V1 is proportional to Z1,
Dialogue: 0,0:01:18.56,0:01:26.01,Default,,0000,0000,0000,,and V2 is equal to Vs times\NZ2 over Z1 plus Z2.
Dialogue: 0,0:01:26.01,0:01:27.43,Default,,0000,0000,0000,,Lets do an example,
Dialogue: 0,0:01:27.43,0:01:29.50,Default,,0000,0000,0000,,using these values right here.
Dialogue: 0,0:01:29.50,0:01:32.68,Default,,0000,0000,0000,,V1 then is going to equal Vs,
Dialogue: 0,0:01:32.68,0:01:41.14,Default,,0000,0000,0000,,which is 5e_j30 times\NZ1 which is 3 plus j2,
Dialogue: 0,0:01:41.14,0:01:44.32,Default,,0000,0000,0000,,divided by Z1 plus Z2,
Dialogue: 0,0:01:44.32,0:01:52.18,Default,,0000,0000,0000,,or 3 plus j2 plus 5 minus j.
Dialogue: 0,0:01:53.15,0:01:56.25,Default,,0000,0000,0000,,Put some parentheses in there.
Dialogue: 0,0:01:56.25,0:01:59.22,Default,,0000,0000,0000,,When we go through and do the math on that,
Dialogue: 0,0:01:59.22,0:02:15.34,Default,,0000,0000,0000,,we get product of those\Nis 2.24e_j56.57 degrees.
Dialogue: 0,0:02:15.34,0:02:24.14,Default,,0000,0000,0000,,Similarly, V2 then is going to\Nequal 5e_j30 just Vs times Z2,
Dialogue: 0,0:02:24.14,0:02:29.64,Default,,0000,0000,0000,,which is 5 minus j\Ndivided by the sum of Z1,
Dialogue: 0,0:02:29.64,0:02:36.69,Default,,0000,0000,0000,,Z2, or 3 plus j2 plus 5 minus j.
Dialogue: 0,0:02:36.69,0:02:47.46,Default,,0000,0000,0000,,When you do those calculations and you\Nget that V2 is equal to 3.16e_j11.57.
Dialogue: 0,0:02:49.42,0:02:59.52,Default,,0000,0000,0000,,I'll leave it to you to show\Nthat V1 plus V2 does in fact equal 5e_j30.