1
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>> Closely related to

2
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the series combination of two impedances
is concept of voltage division.

3
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We saw voltage division back when we were
talking about resistances in series,

4
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and it probably shouldn't surprise
anybody when we see that,

5
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just that the voltage
division with impedances in

6
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the sinusoidal steady state
are of the same type of

7
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calculation as they were when we were
dealing with resistances in series.

8
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The only difference, again, is
that we are using complex numbers.

9
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So, for example, we have then V1 is equal

10
00:00:34,280 --> 00:00:43,030
to Vs times Z1 over Z1 plus Z2,

11
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and that would be the voltage
across this impedance,

12
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and V2 is equal to

13
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Vs times Z2 over Z1 plus Z2.

14
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Of course, it's pretty easy to show
that combining V1 plus V2 equals Vs.

15
00:01:05,355 --> 00:01:09,360
So, what we're saying is that you've
got a total of Vs dropped across there,

16
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Z1 over Z1 plus Z2 times Vs is V1,

17
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or V1 is proportional to Z1,

18
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and V2 is equal to Vs times
Z2 over Z1 plus Z2.

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Lets do an example,

20
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using these values right here.

21
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V1 then is going to equal Vs,

22
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which is 5e_j30 times
Z1 which is 3 plus j2,

23
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divided by Z1 plus Z2,

24
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or 3 plus j2 plus 5 minus j.

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Put some parentheses in there.

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When we go through and do the math on that,

27
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we get product of those
is 2.24e_j56.57 degrees.

28
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Similarly, V2 then is going to
equal 5e_j30 just Vs times Z2,

29
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which is 5 minus j
divided by the sum of Z1,

30
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Z2, or 3 plus j2 plus 5 minus j.

31
00:02:36,690 --> 00:02:47,460
When you do those calculations and you
get that V2 is equal to 3.16e_j11.57.

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I'll leave it to you to show
that V1 plus V2 does in fact equal 5e_j30.