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

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 $R_{Th}$.

Resistors in series have equivalent currents across them.

Norton Equivalent Circuits

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

Credit: EECS 16B Note 0B

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 $I_{No}$.

Resistors in parallel have the same voltage.