WEBVTT

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>> In the next few videos, we're
going to extend the concepts of

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equivalent circuits into the phasor domain,

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in terms of impedances and
phasor voltages and phasor currents.

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So to do that,

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we're going to start by looking
at the source transformations,

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transforming a voltage source with

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a series impedance into a current source
with a parallel impedance and back.

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Then we'll also extend the concept of

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Thevenin equivalent circuits to include
phasors and complex impedances.

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So by review, what we mean when we
say two circuits are equivalent,

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we mean that they have in this case
the same terminal characteristics.

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By that we mean that
an external circuit connected to

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a voltage source with a series
impedance will experience

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the same voltage and current
as that same external circuit

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would experience if it were connected
to a parallel current source,

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connected in parallel with an impedance.

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Both instances, we're going to have
the source impedance be the same value,

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and what we wanted to do is
determine the relationship between

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V sub s and I sub s.

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So that loads or

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external circuits connected to either

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of these would not be able
to tell the difference.

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So they have the same
terminal characteristics.

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That means same voltage and same current.

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To accomplish that, this load here
is going to experience the same V,

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what reference V12, the voltage from

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node one to node two in both the circuits.

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In other words, this V12 and
this V12 will be the same.

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So to do that,

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we need to have the open-circuit voltage.

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The voltage that you would
experience if there was

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no load connected here to be the same.

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In this case, since it's
open circuit there'll be

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no current flowing through here,

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and the voltage V12 will simply equal V,

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the open circuit will equal

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V sub s. Down here when
the terminals one and two are open,

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no current is coming this way.

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So in this case, all of
the current from the source is

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going through this parallel impedance,

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and the voltage that you
would then measure here,

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this V open circuit,

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would equal just I sub s times
Z sub s. From this then,

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we can write directly what
the relationship needs to be.

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In order for these two open-circuit
voltages to be the same,

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this V_OC which is V sub s,

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must equal this open- circuit voltage here,

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I sub s times Z sub s. So in transforming

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a current source with

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a parallel impedance into
a voltage source with a series impedance,

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the voltage source here
would be equal to I sub

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s times Z sub s. Simply rearranging it,

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we can come up with
an expression for I sub s in

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terms of V sub s. That would
be I sub s equals V sub s

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over Z sub s. So if we had
a series voltage source and impedance,

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we could replace those with a parallel
current source and impedance.

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If I sub s here was equal to
the quantity V sub s divided by Z sub s,

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we get a little bit better
feel for that by looking

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at what is referred to as
the short circuit current.

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If you short this out here
and call it I short circuit,

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we should expect to experience
the same I short circuit,

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the same current through this short here.

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Well in this circuit here,

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I short circuit, in other words
zero resistance there,

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the current there is just
going to be V sub s divided by

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Z sub s. On the other hand down
here with this being shorted,

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it shorts out the impedance and so
none of the current goes through here.

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The short-circuit current then would
be simply I sub s or I short circuit

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equals I sub s. Here we then see that in
order for these two to be equivalent,

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I sub s equals V sub s over
Z sub s as we saw there.