# Thevenin Equivalent Resistance

## Thévnin’s Theorem

Using a Thévnin equivalent circuit to model the behavior of a black-box circuit, from the point of view of the two terminals, A and B

Thévnin’s Theorem is a life-saver when you start chaining circuits together. It says that however complex your circuit involving currents, voltages, resistors, capacitors, inductors, etc., it can all be modeled from the point of view of two output or input terminals as a single voltage and a single series impedance (if you haven’t see impedances discussed yet, just read "resistance" where "impedance" is used). This is incredible, because it means that you can completely describe the impact on your circuit of any upstream or downstream electronics just by using these two quantities: the equivalent voltage, and the equivalent impedance.

If you just accept this as true (and it is!), then calculating these quantities is easy. First, for two terminals A and B, calculate or measure the voltage between them if you leave them unconnected. This is the Thévnin equivalent voltage, or ${\displaystyle V_{th}}$. Next, calculate or measure the current that flows between A and B if you connect them with a wire. (Warning, if you are measuring, you might want to put a resistor in series before you blow your fuse!) If you are considering complex impedances, you’ll have to measure current as a function of frequency. Using Ohm’s Law, you then have your Thévnin equivalent impedance, or ${\displaystyle Z_{th}}$ (or ${\displaystyle R_{th}}$ if we are just considering resistance). Done!