# What is Thevenin theorem

Many electronic circuits contain a combination of batteries, resistors and make it very complicated. So simplifying these complex circuits we need Thevenin's Theorem. This theorem states that it is possible to simplify any linear circuits, to an equivalent circuit with just a single voltage source and impedance in series with the load, no matter how complex they are.

## Thevenin theorem statements

_{TH}) in series with an impedance (R

_{TH}), where (V

_{TH}) is the open-circuit voltage between the terminals of the network and (R

_{TH}) is the impedance measured between the terminals with all the energy sources replaced by their internal impedances.

### Thevenin's equivalent circuit

To show the Thevenin's equivalent circuit we consider a circuit with a complicated passive network driven by an energy source (V

_{s}). The network contains three resistors (R

_{1}, R

_{2}, and R

_{3}) and they are connected with a load (R

_{L}). This circuit will be replaced by an equivalent circuit with a voltage source (V

_{TH}) called Thevenin's voltage and impedance (R

_{TH}) called Thevenin's impedance.

_{2}). So the Thevenin's voltage is

_{L}) also disconnected.

Here the load current for this equivalent circuit is

### Steps to follow for solving Thevenin's Theorem

__Step 1__:Identify the load (R

_{L}).

__Step 2__:Remove the load and calculate the open-circuit voltage (V

_{TH}).

__Step 3__:To calculate Thevenin's impedance (R

_{TH}), replace the sources by their internal impedance.

__Step 4__:Construct the Thevenin's equivalent circuit by connecting (V

_{TH}) in series with (R

_{TH}).

### Thevenin's Theorem solved problems

**Exam**

**ple 1:**Calculate the current through the resistor of resistance 6 Ω.

**Solution :**_{L}) = 6 Ω

_{TH}) :

_{TH}) :

Thevenin's equivalent circuit :

**Example 2:**Calculate the Thevenin's voltage and Thevenin's resistance.

To calculate (R

_{TH}) :

**Example 3:**Calculate the current through the load resistance (R

_{L}) = 5 Ω.

**Solution :**_{L}) = 5 Ω

_{TH}) :

Where

And the current through the second loop is

Where

∴ The Thevenin's voltage is

To calculate (R

_{TH}) :

Thevenin's equivalent circuit :