Thevenin’s Theorem: Circuit Simplification

Why Simplify Circuits?

Analysing complex electrical circuits can be challenging. Thevenin’s Equivalence Principle(originally published in his 1833 book Sur un nouveau théorème d’électricité dynamique) states that any number of Voltage sources, and resistors can be modelled by a single voltage source and resistor. In essence this provides an easy way to simplify any linear electrical network into an equivalent circuit composed of just a single voltage source and a single series resistor. Typically in electrical engineering this is called the Rth. This simplification is immensely useful, especially when you need to analyse how different loads affect a complex circuit.

The Thevenin Equivalent Circuit

The core of Thevenin’s Theorem is replacing a complex “black box” network with two components:

• Thevenin Voltage (Vth): This is the open-circuit voltage measured across the two output terminals of the original circuit.
• Thevenin Resistance (Rth): Is the equivalence to all resistances in the circuit summed together into a single resistance. By connecting this resistor in series with the voltage source we can know the manner in which the entire circuit will behave. you can see this in action using the interactive option down bellow.

Once you have Vth and Rth, you can attach any load resistor to this simple equivalent circuit and easily calculate the current and voltage through that load using Ohm’s Law as discussed in out previous lessons. if a resistor is connected directly to ground the it and the Rth will act as a potential divider.