Circuit Theory/Thevenin-Norton

 

Vth using NodeEdit

opening load, finding V_th using Node .. code

${\displaystyle V_{th}=6.4516}$

In using NodeEdit

shorting load, finding I_n using Node .. code

${\displaystyle I_{N}=1.064773736}$

Rth or RnEdit

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

Finding Rth using source injection and nodeEdit

• 

  zero sources to find Rth

 
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  add source injection since parallel/series combinations do not exist

 
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  redraw up and down before solving

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

Comparing Node with Thevenin EquivalentEdit

solving using Node .. code

solving using Thevenin equivalent

Solving the node equations yields:

${\displaystyle V_{a}=5.393}$

${\displaystyle V_{b}=1.1673}$

${\displaystyle V_{c}=1.107}$

${\displaystyle i_{12}=0.3571}$

${\displaystyle v_{12}=4.286}$

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

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

${\displaystyle v_{12}=6.4516*{\frac {12}{6.0591+12}}=4.287}$

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.

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.