[<< wikibooks] Circuit Theory/Thevenin-Norton
== Vth using Node ==

V

t
h

=
6.4516

{\displaystyle V_{th}=6.4516}

== In using Node ==

I

N

=
1.064773736

{\displaystyle I_{N}=1.064773736}

== Rth or Rn ==

V

t
h

/

I

N

=

6.4516
1.064773736

=
6.0591
o
h
m
s

{\displaystyle V_{th}/I_{N}={\frac {6.4516}{1.064773736}}=6.0591ohms}

== Finding Rth using source injection and node ==

Here is the mupad/matlab code that generates the answer Rth = 6.0591 ohms.

== Comparing Node with Thevenin Equivalent ==

Solving the node equations yields:

V

a

=
5.393

{\displaystyle V_{a}=5.393}

V

b

=
1.1673

{\displaystyle V_{b}=1.1673}

V

c

=
1.107

{\displaystyle V_{c}=1.107}

i

12

=
0.3571

{\displaystyle i_{12}=0.3571}

v

12

=
4.286

{\displaystyle v_{12}=4.286}
Using the Thevenin equivalent (and voltage divider) to compute voltage across the 12 ohm resistor:

v

12

=

V

s

∗

12

R

t
o
t
a
l

{\displaystyle v_{12}=V_{s}*{\frac {12}{R{total}}}}

v

12

=
6.4516
∗

12

6.0591
+
12

=
4.287

{\displaystyle v_{12}=6.4516*{\frac {12}{6.0591+12}}=4.287}
So they match ...
Thevenin voltage and resistance can not be computed from a node analysis of the entire circuit, but the node analysis of the entire circuit can be used to check if the thevenin equivalent produces the same numbers.