>> We're going to continue on with our discussion of impedance in
this Phasor Domain analysis of
circuits that are operating the sinusoidal steady-state.
More particularly, we're going to introduce the concept of
complex impedance where we'll see that impedance in
general has a real part and
an imaginary part and can be represented in either
rectangular coordinates or in polar coordinates.
We'll then go on and extend our understanding or
expand our understanding of series and
parallel connections to include impedance and
look at how the concept of voltage and current division apply with impedances.
Then, we'll look at Delta to Wye transformations involving impedances.
So, we've seen that the impedance of
a resistor Z sub R is simply equal to the value of the resistance.
It's a real quantity.
On the other hand, we've seen that the inductor,
impedance of an inductor is equal to j times omega times L,
and it's an imaginary number.
Similarly, Z sub C is equal to negative J
over omega C. Again, an imaginary number.
We observe, and let's reiterate that
the impedance of an inductor is a positive quantity
while the impedance of a capacitor is a negative quantity.
In general, we will talk about Z,
a complex number that will have a real part and an imaginary part.
The real part we're going to refer to as resistance,
the imaginary part we're going to refer to as reactance.
Again, a positive reactance refers to an inductive or an impedance,
it has an inductive nature,
and a negative reactance has a capacity of nature.
Now, we can also talk about Z in
polar coordinates where z then can also be referred to as,
or Z equals magnitude of Z E to the j theta,
where the magnitude of Z is equal to the square root
of R squared plus X squared,
and theta is equal to the arctangent of the imaginary part,
the reactance divided by the resistance.
For example, if we have a resistor and inductor in series with each other,
the net impedance would be then R plus
J omega L. If you add a resistor and a capacitor,
you'd have R minus j times 1 over omega C squared.
In those instances where you have
both an inductor and a capacitor being combined,
the impedance will be pure imaginary and it'll equal J
times the positive impedance of
the inductor minus the impedance of the capacitor.
When this quantity is positive,
we'll say that the impedance has a net inductive characteristic.
When this quantity here is negative,
we'll say that the overall effect or that the overall nature of
this combination here would be net capacitive.
Now, there are times when it's convenient to talk about
not impedance but 1 over the impedance.
So the impedance is a measure of
the circuit's tendency to impede the flow of electrons.
One over the impedance becomes a measure of
the circuit's ability to conduct electrons.
We refer to that as,
call it capital Y and it's referred to as admittance.
It also is a complex quantity consisting of
a real part G that is called conductance,
and j times an imaginary part B, where B,
the imaginary part of the admittance is called or is referred to
as the susceptance, S-U-S-C-E-P-T-A-N-C-E.
So we have impedance in polar or rectangular form.
We have admittance in rectangular form and of course,
it can also be written in polar form also.