Circuit Theory/Thevenin-Norton

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Vth using Node[edit]

opening load, finding Vth using Node .. code
V_{th} = 6.4516

In using Node[edit]

shorting load, finding In using Node .. code
I_N = 1.064773736

Rth or Rn[edit]

V_{th}/I_N= \frac{6.4516}{1.064773736} =  6.0591 ohms

Finding Rth using source injection and node[edit]

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

Comparing Node with Thevenin Equivalent[edit]

solving using Node .. code
solving using Thevenin equivalent

Solving the node equations yields:

V_a = 5.393
V_b = 1.1673
V_c = 1.107
i_{12} = 0.3571
v_{12} = 4.286

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

v_{12} = V_s*\frac{12}{R{total}}
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.