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>> Closely related to

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the series combination of two impedances[br]is concept of voltage division.

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We saw voltage division back when we were[br]talking about resistances in series,

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and it probably shouldn't surprise[br]anybody when we see that,

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just that the voltage[br]division with impedances in

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the sinusoidal steady state[br]are of the same type of

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calculation as they were when we were[br]dealing with resistances in series.

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The only difference, again, is[br]that we are using complex numbers.

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So, for example, we have then V1 is equal

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to Vs times Z1 over Z1 plus Z2,

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and that would be the voltage[br]across this impedance,

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and V2 is equal to

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Vs times Z2 over Z1 plus Z2.

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

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So, what we're saying is that you've[br]got a total of Vs dropped across there,

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Z1 over Z1 plus Z2 times Vs is V1,

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or V1 is proportional to Z1,

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and V2 is equal to Vs times[br]Z2 over Z1 plus Z2.

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Lets do an example,

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using these values right here.

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V1 then is going to equal Vs,

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which is 5e_j30 times[br]Z1 which is 3 plus j2,

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divided by Z1 plus Z2,

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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,

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we get product of those[br]is 2.24e_j56.57 degrees.

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Similarly, V2 then is going to[br]equal 5e_j30 just Vs times Z2,

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which is 5 minus j[br]divided by the sum of Z1,

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Z2, or 3 plus j2 plus 5 minus j.

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When you do those calculations and you[br]get that V2 is equal to 3.16e_j11.57.

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