WEBVTT

00:00:00.000 --> 00:00:02.370
>> Converting impedances from

00:00:02.370 --> 00:00:05.220
a delta connection to

00:00:05.220 --> 00:00:08.189
a Y connection or from a Y
connection to a delta connection,

00:00:08.189 --> 00:00:13.095
is analogous to what we saw when we
were dealing strictly with resistances.

00:00:13.095 --> 00:00:16.630
Again, what we mean when
we say that one say that

00:00:16.630 --> 00:00:21.285
Y circuit is consistent or is
equivalent to a delta connection.

00:00:21.285 --> 00:00:25.535
By that, we mean that the impedance

00:00:25.535 --> 00:00:32.420
seen looking in between
any two terminals is the same,

00:00:32.420 --> 00:00:37.670
whether it is connected in Y or

00:00:37.670 --> 00:00:40.040
connected in delta and when you

00:00:40.040 --> 00:00:42.800
compare these with those that we saw
with working with straight resistances,

00:00:42.800 --> 00:00:48.035
you'll see that
the same relationships hold.

00:00:48.035 --> 00:00:53.110
On this side here we have the Y to

00:00:53.110 --> 00:00:56.570
delta connection and
here we have converting

00:00:56.570 --> 00:01:00.860
delta connected load to a Y connected load.

00:01:00.860 --> 00:01:05.500
So, the Y connected load impedances
are Z_1, Z_2 and Z_3.

00:01:05.500 --> 00:01:09.200
The delta connected as Z_a, as Z_b and Z_c,

00:01:09.200 --> 00:01:14.325
where Z_1 is connected to node one,

00:01:14.325 --> 00:01:16.410
Z_2 is connected to node two,

00:01:16.410 --> 00:01:20.215
Z_3 is connected to node three and Z_a

00:01:20.215 --> 00:01:25.230
is the impedance opposite
the number one terminal,

00:01:25.230 --> 00:01:28.895
Z_b is the impedance opposite
the number two terminal

00:01:28.895 --> 00:01:34.435
and Z_c is the impedance
opposite the third terminal.

00:01:34.435 --> 00:01:36.719
Now, these become interesting,

00:01:36.719 --> 00:01:41.545
even more interesting than they
already are and the circumstances when

00:01:41.545 --> 00:01:46.880
Z_1 equals Z_2 equals Z_3 or you
got a balanced three-phase load.

00:01:46.880 --> 00:01:51.180
Under those circumstances, when Z_1

00:01:51.180 --> 00:01:56.940
equals Z_2 equals Z_3, we'll call that Z_y.

00:01:56.940 --> 00:01:59.474
When that is the case,

00:01:59.474 --> 00:02:06.735
then Z_a equals Z_b equals Z_c.

00:02:06.735 --> 00:02:11.970
We'll call that Z Delta is equal to.

00:02:11.970 --> 00:02:15.720
If this Z is the same, you have one, two,

00:02:15.720 --> 00:02:21.020
three, Z_y squared divided by Z_y.

00:02:21.020 --> 00:02:27.130
So, Z Delta then is equal
to three times Z_y,

00:02:27.130 --> 00:02:30.650
and over here you do
a similar situation where

00:02:30.650 --> 00:02:35.770
Z_a equals Z_b equals Z_c equals,

00:02:35.770 --> 00:02:37.670
call that again Z delta,

00:02:37.670 --> 00:02:42.780
then Z_1 equals Z_2 equals Z_3,

00:02:42.780 --> 00:02:46.890
call that Z_y and that is then here

00:02:46.890 --> 00:02:51.515
you'd have Z Delta squared
over three Z delta,

00:02:51.515 --> 00:02:57.760
or Z_y then is equal to
Z Delta divided by three.