What is Thevenin's 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


According to this theorem, any two-terminal linear network containing energy sources and impedances can be replaced by an equivalent circuit consisting of a voltage source (VTH) in series with an impedance (RTH).

Thevenin theorem

Where (VTH) is the open-circuit voltage between the terminals of the network and (RTHis the impedance measured between the terminals with all the energy sources replaced by their internal impedances.

Thevenin's equivalent circuit


To show Thevenin's equivalent circuit we consider a circuit with a complicated passive network driven by an energy source (Vs). The network contains three resistors (R1, R2, and R3) and they are connected with a load (RL).



This circuit will be replaced by an equivalent circuit with a voltage source (VTH) called Thevenin's voltage and impedance (RTH) called Thevenin's impedance.

Thevenin theorem

To calculate Thevenin's voltage at first remove the load. When the load has removed the voltage across AB is equal to the voltage across the resistor (R2). So the Thevenin's voltage is


Where I = The flow of current through the circuit when the load is removed.

Now to calculate Thevenin's impedance at first replace the energy sources with their internal impedance and the load (RL) also disconnected.



Note: If the internal impedance of the energy sources is given then it will be added to the resistor network.

Here the internal impedance is zero so the  Thevenin's impedance is



Therefore the Thevenin's equivalent circuit for the above circuit is

Thevenin theorem

Here the load current for this equivalent circuit is




Steps to follow for solving problems by Thevenin's Theorem

Step 1 :

Identify the load (RL).

Step 2 :

Remove the load and calculate the open-circuit voltage (VTH).

Step 3 :

To calculate Thevenin's impedance (RTH), replace the sources with their internal impedance.

Step 4 :

Construct the Thevenin's equivalent circuit by connecting (VTH) in series with (RTH).

Solved problems by Thevenin's Theorem


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

Thevenin theorem

Solution :

To identify the load :

Here the load (RL) = 6 Ω

To calculate Thevenin's voltage (VTH) :
Thevenin theorem

Now remove the load. When the load is removed the open-circuit voltage is the same as that of the voltage across the resistor of resistance 4 Ω.

∴ The current in the circuit is 


∴ The Thevenin's voltage is


To calculate Thevenin's impedance (RTH) :
Thevenin theorem

After replacing the source with their internal impedance the Thevenin's impedance is


Thevenin's equivalent circuit :
Thevenin theorem

∴ The current through the load,


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

Thevenin theorem

Solution :

To calculate Thevenin's voltage (VTH) :

Here the open-circuit voltage is the same as that of the voltage across the resistor of resistance 7 Ω.

∴ The current in the circuit is 


∴ The Thevenin's voltage is



To calculate Thevenin's impedance (RTH) :
Thevenin theorem

After replacing the source with their internal impedance the Thevenin's impedance is


Example 3: Calculate the current through the load resistance (RL) = 5 Ω.

Thevenin theorem

Solution :

To identify the load :

Here the load (RL) = 5 Ω

To calculate Thevenin's voltage (VTH) :

Thevenin theorem

Now remove the load. When the load is removed the open-circuit voltage is the same as that of the voltage across the resistor of resistance 10 Ω.

Here the current through the first loop is


Where



And the current through the second loop is



Where




∴ The Thevenin's voltage is



To calculate Thevenin's impedance (RTH) :


Thevenin theorem

After replacing the source with their internal impedance the Thevenin's impedance is


Thevenin's equivalent circuit :
Thevenin theorem

∴ The current through the load,