0:00:00.000,0:00:03.480
>> Now, let's consider how we combine

0:00:03.480,0:00:07.935
impedances that are connected in[br]either series or in parallel.

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We might get a hint from[br]the fact that because

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impedances have the units of ohms,

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we would expect them to combine in

0:00:14.640,0:00:16.680
exactly the same way that resistances

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do and we're going to see[br]that is in fact the case.

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So for example, we've got Z_1 and Z_2[br]connected in series with each other.

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The equivalent impedance Z equivalent[br]is just equal to Z_1 plus Z_2.

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So Z_1 equals 3 plus J_2.

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Three being the real part sometimes[br]referred to as the resistance,

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and J_2 the imaginary part also[br]sometimes referred to as the reactants.

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A second impedance Z_2 equaling 5 minus J,

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then the equivalent impedance of[br]those two connected in series

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will simply be 3 plus J_2 plus 5,

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minus J, which equals 3 plus five is 8.

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J_2 minus J_1 is plus J.

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That's its rectangular form,

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and we can also write[br]that it is parallel form,

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which would give us then[br]8.06 for the magnitude E to

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the J at 7.103.

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All right, now let's look[br]at these two in parallel.

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In parallel, it turns out that as[br]it was with resistance is also

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1 over Z_eq is equal to 1 over Z_1,

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plus 1 over Z_2.

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Now, sometimes we refer[br]to instead of impedances,

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we'll refer to admittances where admittance[br]is called y is equal to 1 over Z.

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So in this case, we could say then[br]that Y_eq equals Y_1, plus Y_2.

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All right. Let's just simplify[br]this in terms of impedances.

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We know then that 1 over Z_eq.

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We need to combine these two terms to get

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the common denominator or to get[br]a common denominator to combine them.

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So it would be the common denominator[br]would be Z_1 times Z_2,

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and in the numerator[br]would have Z_2 plus Z_1.

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Thus that now we can invert them,

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and we get Z_eq is equal[br]to Z_1 Z_2 over Z_1,

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plus Z_2 or the

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product of the impedances divided[br]by the sum of the impedances.

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I'll leave it to you to go ahead[br]and plug in Z_1 and Z_2 on these,

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but let me just give you that[br]for these values of Z_1 and Z_2,

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we get Z_eq is equal to

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2.2 plus 0.6J in rectangular coordinates,

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and in parallel coordinates that turns

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out to be around a site[br]in polar coordinates.

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That turns out to be 2.28 e to

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the positive J15.3 degrees.