L7 4 4 Delta Wye Connections

Delta and wye connnected impedances

>> Converting impedances from

a delta connection to

a Y connection or from a Y
connection to a delta connection,

is analogous to what we saw when we
were dealing strictly with resistances.

Again, what we mean when
we say that one say that

Y circuit is consistent or is
equivalent to a delta connection.

By that, we mean that the impedance

seen looking in between
any two terminals is the same,

whether it is connected in Y or

connected in delta and when you

compare these with those that we saw
with working with straight resistances,

you'll see that
the same relationships hold.

On this side here we have the Y to

delta connection and
here we have converting

delta connected load to a Y connected load.

So, the Y connected load impedances
are Z_1, Z_2 and Z_3.

The delta connected as Z_a, as Z_b and Z_c,

where Z_1 is connected to node one,

Z_2 is connected to node two,

Z_3 is connected to node three and Z_a

is the impedance opposite
the number one terminal,

Z_b is the impedance opposite
the number two terminal

and Z_c is the impedance
opposite the third terminal.

Now, these become interesting,

even more interesting than they
already are and the circumstances when

Z_1 equals Z_2 equals Z_3 or you
got a balanced three-phase load.

Under those circumstances, when Z_1

equals Z_2 equals Z_3, we'll call that Z_y.

When that is the case,

then Z_a equals Z_b equals Z_c.

We'll call that Z Delta is equal to.

If this Z is the same, you have one, two,

three, Z_y squared divided by Z_y.

So, Z Delta then is equal
to three times Z_y,

and over here you do
a similar situation where

Z_a equals Z_b equals Z_c equals,

call that again Z delta,

then Z_1 equals Z_2 equals Z_3,

call that Z_y and that is then here

you'd have Z Delta squared
over three Z delta,

or Z_y then is equal to
Z Delta divided by three.