# Circuit Theory/Thevenin-Norton

## Vth using Node

!opening load, finding V~th~ using Node ..
code

$$V_{th} = 6.4516$$

## In using Node

!shorting load, finding I~n~ using Node ..
code

$$I_N = 1.064773736$$

## Rth or Rn

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

## Finding Rth using source injection and node

<File:Example23d.png%7Czero> sources to find Rth
<File:Example23e.png%7Cadd> source injection since parallel/series
combinations do not exist <File:Example23g.png%7Credraw> up and down
before solving

Here is the mupad/matlab code that generates the
answer R~th~ = 6.0591 ohms.

## Comparing Node with Thevenin Equivalent

!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.

