# Thevenin and Norton Equivalent Circuits

Thévenin’s theorem for linear electrical networks states that any combination of voltage sources, current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. Any unknown circuit containing only resistances, and voltage and current sources can be replaced by a Thévenin equivalent circuit consisting of an equivalent voltage source in a series connection with an equivalent resistance. Norton’s theorem for electrical networks states that any collection of voltage sources and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R. Thevenin and Norton equivalent circuits provide a means to simplify complex electrical circuits by allowing portions of some circuits to be replaced by calculated equivalent values. This reduces the time it takes to calculate how long changes to a load will affect the rest of a circuit. Simplifying equations also reduces the chances for errors. Thevenin’s Theorem is especially useful in analyzing power systems and other circuits where the “load” resistor is subject to change, and re-calculation of the circuit is necessary with each trial value of load resistance, to determine voltage across it and current through it. There are other analysis methods that can be used to determine voltage across and current through the load resistor. But these methods can be time consuming and would have to be repeated every time the load resistance changed, which is something very common in power systems. Thevenin’s Theorem makes this easy by temporarily removing the load resistance from the original circuit and reducing what’s left to an equivalent circuit composed of a single voltage source and a single, series resistance. The load resistance can then be re-connected to this “Thevenin equivalent circuit” and calculations carried out as if the whole network were nothing but a simple series circuit. The same advantages also apply to Norton’s Theorem. If we wish to analyze load resistor voltage and current, over several different values of load resistance, we can use the Norton equivalent circuit again and again, applying nothing more complex than simple parallel circuit analysis to determine what’s happening with each trial load.