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**__
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**
Power Supply 1-2-3: Direct Current (DC)**

# Chapter 10

# DC
NETWORK ANALYSIS

Since Thevenin's and Norton's Theorems
are two equally valid methods of reducing a complex network down to
something simpler to analyze, there must be some way to convert a
Thevenin equivalent circuit to a Norton equivalent circuit, and vice
versa (just what you were dying to know, right?). Well, the
procedure is very simple.

You may have noticed that the
procedure for calculating Thevenin resistance is identical to the
procedure for calculating Norton resistance: remove all power
sources and determine resistance between the open load connection
points. As such, Thevenin and Norton resistances for the same
original network must be equal. Using the example circuits from the
last two sections, we can see that the two resistances are indeed
equal:

Considering the fact that both
Thevenin and Norton equivalent circuits are intended to behave the
same as the original network in suppling voltage and current to the
load resistor (as seen from the perspective of the load connection
points), these two equivalent circuits, having been derived from the
same original network should behave identically.

This means that both Thevenin and
Norton equivalent circuits should produce the same voltage across
the load terminals with no load resistor attached. With the Thevenin
equivalent, the open-circuited voltage would be equal to the
Thevenin source voltage (no circuit current present to drop voltage
across the series resistor), which is 11.2 volts in this case. With
the Norton equivalent circuit, all 14 amps from the Norton current
source would have to flow through the 0.8 Ω Norton resistance,
producing the exact same voltage, 11.2 volts (E=IR). Thus, we can
say that the Thevenin voltage is equal to the Norton current times
the Norton resistance:

So, if we wanted to convert a Norton
equivalent circuit to a Thevenin equivalent circuit, we could use
the same resistance and calculate the Thevenin voltage with Ohm's
Law.

Conversely, both Thevenin and Norton
equivalent circuits should generate the same amount of current
through a short circuit across the load terminals. With the Norton
equivalent, the short-circuit current would be exactly equal to the
Norton source current, which is 14 amps in this case. With the
Thevenin equivalent, all 11.2 volts would be applied across the 0.8
Ω Thevenin resistance, producing the exact same current through the
short, 14 amps (I=E/R). Thus, we can say that the Norton current is
equal to the Thevenin voltage divided by the Thevenin resistance:

This equivalence between Thevenin and
Norton circuits can be a useful tool in itself, as we shall see in
the next section.

**REVIEW:**
- Thevenin and
Norton resistances are equal.
- Thevenin
voltage is equal to Norton current times Norton resistance.
- Norton current
is equal to Thevenin voltage divided by Thevenin resistance.