Circuit Theory/Thevenin-Norton

Vth using NodeEdit

 
opening load, finding Vth using Node .. code
 

In using NodeEdit

 
shorting load, finding In using Node .. code
 

Rth or RnEdit

 

Finding Rth using source injection and nodeEdit

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

Comparing Node with Thevenin EquivalentEdit

 
solving using Node .. code
 
solving using Thevenin equivalent

Solving the node equations yields:

 
 
 
 
 

Using the Thevenin equivalent (and voltage divider) to compute voltage across the 12 ohm resistor:

 
 

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.