# Thevenin Theorem

The theorization of thevenin is an analytical method used to convert a complex circuit into a simple equivalent circuit consisting of a single resistance in series with a source voltage.

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In the previous three lessons, we looked at solving complex electrical circuits using Kirchhoff's Circuit Laws, Mesh Analysis, and finally Node Analysis.However, there are many more "Circuit Analysis Theorems" to choose from, which can calculate currents and voltages at any point in a circuit.In this course, we will look at one of the more common circuit analysis theorems (next to Kirchhoff), **Thevenin Theorem**.

**Thevenin Theorem**says, *"Any linear circuit containing several voltages and resistance can be replaced in series with only a single voltage with a single resistance connected along the load".*In other words, it is possible to simplify any electrical circuit, no matter how complex, to an equivalent two-terminal circuit with only a single fixed voltage source in series with a load-dependent resistance (or impedance), as shown below.

**Thevenin Theorem is**especially useful for circuit analysis of power or battery systems and other interconnected resistant circuits, where it will have an effect on the adjacent part of the circuit.

As far as we know, in relation to R, _{L} as load resistance, circuit elements and energy sources consist of multiple resistant "single port" network can be substituted with a single total resistance, Rs and individual equal voltage etc. .Rs is the source resistance value that looks back at the circuit, and vs is the open circuit voltage in the terminals.

For example, consider the circuit in the previous tutorials.

First, to analyze the circuit, we need to remove the central 40Ω load resistance connected to the EU terminals and remove any internal resistance associated with voltage sources.This is done by short-circuiting all voltage sources connected to the circuit, that is, by making i = 0 or any connected current source i = 0.This is because we want to have an ideal voltage source or an ideal current source for circuit analysis.

The equivalent resistance value, Rs, is found by calculating the total resistance by looking back from terminals A and B with short circuit of all voltage sources.Then we get the following circuit.

### Finding Equivalent Resistance (Rs)

Voltage Vs is defined as the total voltage between terminals A and B when there is an open circuit between them.So the load resistance is not connected to the R _{L.}

### Finding Equivalent Voltage (Vs)

Now we need to reconnect the two voltages, and the current flowing around the loop as V _{S} = V _{AB} is calculated as follows:

This current of 0.33 amps (330mA) is common to both resistors, so the voltage drop over 20Ω resistance or 10Ω resistance can be calculated as follows:

V _{AB} = 20 – (20Ω x 0.33amp) = 13.33 volts.

or

V _{AB} = 10 + (10Ω x 0.33amps) = 13.33 volts.

Thevenin's Equivalent circuit will then consist of a series of resistance of 6.67Ω and a voltage source of 13.33v.With 40Ω resistance that is reconnected to the circuit, we achieve:

and the current flowing around the circuit is given as follows:

Again, 0.286 amps is the same value – we found it using Kirchhoff's circuit law in previous circuit analysis training.

**The theorism of thevenin**can be used as another type of circuit analysis method and is especially useful in the analysis of complex circuits consisting of one or more voltage or current sources and organized resistors in ordinary parallel and serial connections.

While Thevenin's circuit theorem can be mathematically defined in terms of current and voltage, it is not as powerful as Mesh Current Analysis or Node Voltage Analysis in larger networks, since mesh or node analysis is usually required in any Thevenin exercise, so it can be.However, Thevenin's equivalent Transistor circuits, such as batteries, voltage sources are very useful in circuit design.

## Thevenin Theorem Summary

Here we found that the thevenin theorem is another type of circuit analysis tool that can be used to reduce any complex electrical grid to a simple circuit consisting of a single voltage source, vs. serially Rs .

Looking back at terminals A and B, this single circuit behaves electrically exactly the same as the complex circuit in which it replaces it.In other words, iv relations in EU terminals are the same.

The basic procedure for solving a circuit using the **Thevenin Theorem** is as follows:

**1.**Remove load resistance R_{L}or the corresponding component.**2.**Find the R_{S}by short-circuiting all voltage sources or by open circuiting all current sources.**3.**Find V_{S}with the usual circuit analysis methods.**4.**Find the current that passes through the R_{L}load resistance.

In the next lesson, we will look at the Norton Theorem, which allows a network of linear resistors and resources to be represented by an equivalent circuit with a single current source in parallel with a single source resistance.