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>> All right. In our previous video,

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we found that the Thevenin
equivalent voltage, V_Th,

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was equal to 6.25 angle 51.34 degrees.

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Once again, I'm going to be
using this shorthand notation

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of representing the polar coordinates
of the impedances of the phasors

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as opposed to writing 6.25e to the j51.34.

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All right. With the Thevenin voltage,

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we need now simply to determine

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the Thevenin equivalent impedance

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and we're going to do that
each of three different ways.

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This first method is what we'll refer
to as the Equivalent Impedance method.

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It works when we have
only independent sources or no sources.

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This equivalent impedance method
that we're going to show first

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does not work if the circuit you're
analyzing has dependent sources.

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So, this approach requires us to deactivate
any independent sources present.

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In this case, there's
an independent voltage source here

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which we deactivate by turning it to zero

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and thus replacing it with a short circuit.

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Then, looking back into
the circuit from the terminals AB

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and determining what the equivalent
impedance is that we would see

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looking back in that way.

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Well, hopefully you can see pretty
easily that with the source deactivated-

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replaced with short-circuit,

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it brings this capacitor and
this resistor in parallel,

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-and that parallel combination is
in series with the j50-Ohm resistor

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such that the impedance seen
looking back into these terminals,

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Z Thevenin, will equal Z parallel
plus the j50-Ohm inductor.

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So, Z parallel is equal to

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20 times minus j25 divided by 20 minus j25,

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which turns out to equal
12.2 minus j9.8 Ohms.

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So finally, Z Thevenin then is equal to Zp;

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12.2 minus j9.8 plus the j50,

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and that then equals 12.2 plus j40.2 Ohms.

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Z Thevenin, bringing it up here,

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then rewriting it just to show what
we've got to show our incomplete model.

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Our complete model involves the Z Thevenin
equaling 12.2 plus j40.2 ohms

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and our claim then is that
this Thevenin equivalent circuit

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has the same terminal characteristics
at the AB terminals

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as our original more complicated circuit.