>> Closely related to
the series combination of two impedances is concept of voltage division.
We saw voltage division back when we were talking about resistances in series,
and it probably shouldn't surprise anybody when we see that,
just that the voltage division with impedances in
the sinusoidal steady state are of the same type of
calculation as they were when we were dealing with resistances in series.
The only difference, again, is that we are using complex numbers.
So, for example, we have then V1 is equal
to Vs times Z1 over Z1 plus Z2,
and that would be the voltage across this impedance,
and V2 is equal to
Vs times Z2 over Z1 plus Z2.
Of course, it's pretty easy to show that combining V1 plus V2 equals Vs.
So, what we're saying is that you've got a total of Vs dropped across there,
Z1 over Z1 plus Z2 times Vs is V1,
or V1 is proportional to Z1,
and V2 is equal to Vs times Z2 over Z1 plus Z2.
Lets do an example,
using these values right here.
V1 then is going to equal Vs,
which is 5e_j30 times Z1 which is 3 plus j2,
divided by Z1 plus Z2,
or 3 plus j2 plus 5 minus j.
Put some parentheses in there.
When we go through and do the math on that,
we get product of those is 2.24e_j56.57 degrees.
Similarly, V2 then is going to equal 5e_j30 just Vs times Z2,
which is 5 minus j divided by the sum of Z1,
Z2, or 3 plus j2 plus 5 minus j.
When you do those calculations and you get that V2 is equal to 3.16e_j11.57.
I'll leave it to you to show that V1 plus V2 does in fact equal 5e_j30.