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>> We're going to continue on with[br]our discussion of impedance in

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this Phasor Domain analysis of

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circuits that are operating[br]the sinusoidal steady-state.

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More particularly, we're going[br]to introduce the concept of

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complex impedance where[br]we'll see that impedance in

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general has a real part and

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an imaginary part and can[br]be represented in either

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rectangular coordinates[br]or in polar coordinates.

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We'll then go on and extend[br]our understanding or

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expand our understanding of series and

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parallel connections to[br]include impedance and

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look at how the concept of voltage and[br]current division apply with impedances.

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Then, we'll look at Delta to[br]Wye transformations involving impedances.

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So, we've seen that the impedance of

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a resistor Z sub R is simply equal[br]to the value of the resistance.

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It's a real quantity.

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On the other hand, we've[br]seen that the inductor,

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impedance of an inductor is[br]equal to j times omega times L,

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and it's an imaginary number.

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Similarly, Z sub C is equal to negative J

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over omega C. Again, an imaginary number.

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We observe, and let's reiterate that

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the impedance of an inductor[br]is a positive quantity

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while the impedance of a capacitor[br]is a negative quantity.

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In general, we will talk about Z,

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a complex number that will have[br]a real part and an imaginary part.

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The real part we're going[br]to refer to as resistance,

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the imaginary part we're going[br]to refer to as reactance.

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Again, a positive reactance refers[br]to an inductive or an impedance,

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it has an inductive nature,

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and a negative reactance[br]has a capacity of nature.

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Now, we can also talk about Z in

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polar coordinates where z then[br]can also be referred to as,

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or Z equals magnitude[br]of Z E to the j theta,

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where the magnitude of Z is[br]equal to the square root

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of R squared plus X squared,

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and theta is equal to the arctangent[br]of the imaginary part,

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the reactance divided by the resistance.

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For example, if we have a resistor and[br]inductor in series with each other,

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the net impedance would be then R plus

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J omega L. If you add[br]a resistor and a capacitor,

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you'd have R minus j times[br]1 over omega C squared.

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In those instances where you have

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both an inductor and[br]a capacitor being combined,

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the impedance will be pure[br]imaginary and it'll equal J

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times the positive impedance of

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the inductor minus[br]the impedance of the capacitor.

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When this quantity is positive,

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we'll say that the impedance has[br]a net inductive characteristic.

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When this quantity here is negative,

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we'll say that the overall effect[br]or that the overall nature of

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this combination here[br]would be net capacitive.

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Now, there are times when[br]it's convenient to talk about

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not impedance but 1 over the impedance.

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So the impedance is a measure of

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the circuit's tendency to[br]impede the flow of electrons.

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One over the impedance becomes a measure of

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the circuit's ability to conduct electrons.

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We refer to that as,

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call it capital Y and it's[br]referred to as admittance.

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It also is a complex quantity consisting of

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a real part G that is called conductance,

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and j times an imaginary part B, where B,

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the imaginary part of the admittance[br]is called or is referred to

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as the susceptance, S-U-S-C-E-P-T-A-N-C-E.

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So we have impedance in[br]polar or rectangular form.

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We have admittance in[br]rectangular form and of course,

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it can also be written in polar form also.