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_L by using Thevenin’s theorem.

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_oc is calculated.

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_s 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.

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_oc) across the open-circuited load terminals.

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 Ω using Thevenin’s Theorem.