L7 4 0 Complex Impedance

>> 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.