> For the complete documentation index, see [llms.txt](https://veriny.gitbook.io/berkeley/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://veriny.gitbook.io/berkeley/eecs16b/thevenin-and-norton-equivalence.md).

# Thevenin and Norton Equivalence

Adapted from 16B notes.

## Resistors in Series and in Parallel

Resistors in parallel and in series can be simplified as follows.

$$
R\_{\sum series} = R\_1 + R\_2 + R\_3 + ... + R\_n \\
R\_{\sum parallel} =  (\frac{1}{R\_1} + \frac{1}{R\_2} + \frac{1}{R\_3} + ... +  \frac{1}{R\_n})^{-1}
$$

## Thevenin Equivalent Circuits

Thevenin equivalent circuits are circuits that contain a voltage source and a resistor.

![Credit: EECS 16B Note 0B](https://2947382171-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M6XPH5Qvmbnhx_A2DDH%2F-MRUShKlnq6vUyjhPRH7%2F-MRUSittdId13niAgAsY%2Fimage.png?alt=media\&token=c00f62d9-7f09-4493-b258-a283dd1392ec)

You can find the values, $$R\_{Th}$$ and $$V\_{Th}$$, as follows. Assume that you're finding the Thevenin equivalent of Ckt A.

* Find the voltage across the terminals of Ckt A. This is $$V\_{Th}$$.
* Find the equivalent resistances of the elements in Ckt A.  This is the value of $$R\_{Th}$$.

{% hint style="success" %}
Resistors in series have equivalent currents across them.
{% endhint %}

## Norton Equivalent Circuits

Norton equivalent circuits are circuits that contain a current source and a resistor in parallel. 

![Credit: EECS 16B Note 0B](https://2947382171-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M6XPH5Qvmbnhx_A2DDH%2F-MRUShKlnq6vUyjhPRH7%2F-MRUSituwawBuj1UR7nP%2Fimage.png?alt=media\&token=57b7ee0e-cc3a-4fbd-87e2-54657a76ece3)

You can find the values, $$R\_{No}$$ and $$I\_{No}$$, as follows. Assume that you're finding the Norton equivalent of Ckt A.

* Find the voltage across the terminals of Ckt A. This is $$R\_{No}$$. Note that$$R\_{Th} = R\_{No}$$!
* Find the current flowing into Ckt A. This is $$I\_{No}$$.

{% hint style="success" %}
Resistors in parallel have the same voltage.
{% endhint %}