In this article, we will discuss Thevenin’s Theorem, its statement, explanation, steps to solve a circuit, and numerical examples.

**Thevenin’s theorem**
is one of the most extensively used network theorems which was given by **M. L. Thevenin**, the French engineer. This
theorem is used to simplify complicated electric circuits. When we are
interested in a particular part of a big circuit. Thevenin’s theorem is applied
where it is required to determine the current through or voltage across any one
circuit element in a circuit without going through the complex method of
solving a set of circuit equations. Now, let us discuss the statement of
Thevenin’s theorem.

# Thevenin’s Theorem Statement

The **statement of
Thevenin’s theorem** is as under:

Any linear electric circuit consisting of independent and/or
dependent voltage sources and current sources, and linear bilateral circuit
elements can be replaced by an equivalent circuit consisting of a voltage
source in series with a resistor, where the voltage of the voltage source will
be the open-circuited voltage across the open-circuited load terminals and the
resistance of the series resistor will be the internal resistance of the source
network looking through the open-circuited load terminals.

In simple words, any two-terminal linear bilateral complex electric
circuit can be replaced by an equivalent circuit consisting of a voltage source
and a series resistor.

# Thevenin’s Theorem Explanation

We can explain Thevenin’s theorem with the help of an electric
circuit. For that let us consider a simple DC circuit as shown in figure-1.

In this circuit, we are to find the electric current *I _{L}* through the load resistor

*R*by using Thevenin’s theorem.

_{L}As we know, in Thevenin’s theorem, the given electric
circuit is replaced by a voltage source and series resistor. In order to
determine the value of the voltage source, the load resistor *R _{L}* is to be removed from the circuit, and then

*V*is calculated.

_{oc}Refer to the electric circuit shown in figure-2, we have,

`\V_(oc)=IR_2`

`\⇒V_(oc)=(V_s/(R_1+R_2 )) R_2`

The open-circuited voltage *V _{oc}* is also called

**Thevenin’s voltage**and is denoted by

*V*.

_{Th}Next, in order to determine the value of
internal resistance (i.e. series resistance of the Thevenin’s equivalent
circuit, called **Thevenin’s Resistance**)
in series with the voltage *V _{oc}*,
the voltage source

*V*is removed (i.e. deactivated by a short circuit since it does not have any internal resistance). Then, the equivalent resistance of the network is calculated by looking at the open-circuited terminals.

_{s}Refer to the network shown in figure-3, we have,

`\R_(Th)=((R_1 R_2)/(R_1+R_2 ))+R_3`

Now, according to Thevenin’s theorem, the
equivalent electric circuit will be as shown in figure-4.

The electric current through the load resistor will be,

`\I_L=V_L/(R_(Th)+R_L )`

In this way, a given complex electric
circuit can be converted into its equivalent Thevenin’s circuit.

Now, let us record the process we followed in explaining Thevenin’s theorem to obtain the step-by-step
procedure to solve an electric circuit using Thevenin’s theorem.

# Thevenin's Theorem Step-by-Step Procedure

We can convert a complex electric circuit into its
equivalent Thevenin’s circuit by following these four steps:

**Step (1)** – Remove
the load resistor (*R _{L}*) and
calculate the open circuit voltage (

*V*) across the open-circuited load terminals.

_{oc}**Step (2)** – Remove
(deactivate) the constant sources. To deactivate the ideal voltage source, remove
it by a short circuit. To deactivate the ideal current source, remove it by opening the circuit.
If the voltage source and current source are practical, then remove them by their
internal resistance. Then, find the internal resistance (Thevenin’s resistance)
*R _{Th}* of the network by
looking through the open-circuited load terminals.

**Step (3)** – Obtain
the Thevenin’s equivalent circuit by connecting Thevenin’s resistance *R _{Th}* in series with the open
circuit voltage

*V*.

_{oc}**Step (4)** –
Reconnect the load resistor R_{L} across the load terminal and
calculate the load current and load voltage.

# Thevenin’s Theorem Limitations

There are some limitations of Thevenin’s theorem. Thevenin’s
theorem is not applicable in the following conditions:

- Thevenin’s theorem cannot be applied to an electric circuit with a source coupling between the load network and the source network. This means that there is a dependent energy source in the source network whose magnitude depends upon the current or voltage of any element in the load network. Then, Thevenin’s theorem cannot be applied to such circuits.
- Thevenin’s theorem cannot be applied to an electric circuit if there is no mutual coupling or transfer coupling between the elements of the source network and load network.

Finally, let us discuss some solved numerical examples to understand how we can apply Thevenin’s theorem to a practical electric circuit to obtain the solution.

**Numerical Example**
– Find the current through the load resistor *R _{L}
=* 5 Î© using Thevenin’s
Theorem.

**Solution** – We can find the electric
current through *R _{L}* by
using Thevenin’s theorem as follows:

**Step 1** – Remove the load resistance *R _{L}*, and calculate the voltage
across the open-circuited load terminals.

`\V_(Th)=12×6/(4+6)=7.2" V"`

**Step 2** – Deactivate the voltage source of 12
volts, and find Thevenin’s resistance R_{Th}.

`\R_(Th)=((4×6)/(4+6))+4=6.4 Î©`

**Step 3** – Replace the network with its
Thevenin equivalent circuit and connect the load resistance R_{L},
and calculate the load current.

`\I_L=V_(Th)/(R_(Th)+R_L)`

`\⇒I_L=7.2/(6.4+5)=0.63" A"`

Hence,
this is all about Thevenin’s theorem, its statement, explanation, and numerical
examples.