Thevenin theorem states that any combination of voltage sources, current sources, and resistors with two terminals for a linear electric circuit is electrically equivalent to a single voltage source (V) and series resistor (R). The theorem can also be applied to general impedances, not just resistors for single frequency AC systems. Any complex circuit can be represented by a Thevenin’s equivalent circuit consisting of a single voltage source and series resistance connected to a load.

Table of Contents

## Thevenin Theorem

**Any two-terminal DC network can be replaced by an equivalent circuit consisting of only a voltage source and a series resistor.**

In other words, the current flowing through a resistor connected across any two terminals of a network by an equivalent circuit having a voltage source E_{th} in series with a resistor R_{th}. Where E_{th} is the open-circuit voltage between the required two terminals called the Thevenin voltage and the R_{th} is the equivalent resistance of the network as seen from the two-terminal with all other sources replaced by their internal resistances called Thevenin resistance

### Thevenin Equivalent Circuit

Let us consider a simple DC circuit as shown in the figure above, where we have to find the load current I_{L} by the Thevenin theorem. In order to find the equivalent voltage source, R_{L} is removed from the circuit as shown in the figure below and V_{TH} is calculated

Now, to find the internal resistance of the network (Thevenin’s resistance or equivalent resistance) in series with the open-circuit voltage V_{OC}, also known as Thevenin’s voltage V_{TH}, the voltage source is removed or we can say it is deactivated by a short circuit (as the source does not have any internal resistance) as shown in the figure below

As per the Thevenin Statement, the load current is determined by the circuit shown above and the equivalent Thevenin’s circuit is obtained. The load current I_{L} is given as

Where

V_{TH} is the Thevenin’s equivalent voltage. It is an open circuit voltage across the load terminal AB.

R_{TH} is the Thevenin’s equivalent resistance, as seen from the load terminals where all the sources are replaced by their internal impedance.

R_{L} is the load resistance.

#### Step of Thevenin Theorem

**Step 1 –** At first remove the load resistance R** _{L}** of the given circuit.

**Step 2 – **By the internal resistance replace all the impedance sources.

**Step 3 –** If the sources are ideal then short circuit the voltage source and open the current source.

**Step 4 –** Now find the equivalent resistance at the load terminals know as Thevenin’s Resistance (R_{TH}).

**Step 5 –** Draw the Thevenin’s equivalent circuit by connecting the load resistance and after that determine the desired response.

## Application Of Thevenin Theorem

- It is very useful for analyzing power systems and other circuits where one particular load resistor in the circuit and re-calculation of the circuit is essential with each trial value of load resistance, to find the voltage across it and current through it.
- Source modeling and resistance measurement by using the Wheatstone bridge provide applications for Thevenin’s theorem.

## Practical Limitation

- If circuits are not only linear over an indicated range of values, thus the Thevenin equivalent is valid only within this linear range and may not be valid outside the range.
- The Thevenin equivalent has an equivalent I-V characteristic only from the point of view of the load.
- The power waste of the Thevenin equivalent is not necessarily similar to the power dissipation of the real system. whatever, the power waste by an external resistor between the two output terminals is similar but the internal circuit is represented.

**Example**

For example, consider the following circuit;

At first, we have to remove the center 40Ω resistor and short out (not physically as this would be dangerous) all the emf’s connected to the circuit, or open circuit any current sources. The value of Rs is found by calculating the total resistance at the terminals A and B with all the emf’s removed, and the value of the Vs is the total voltage across the terminals A and B with an open circuit and no load resistor connected. Then, we get the following circuit

**Find Equivalent Resistance (R _{T}):**

10ΩResistor in parallel with the 20ΩResistor

**Find Equivalent Voltage (Vs):**

We now need to reconnect the two voltages back into the circuit, and as V_{S} = V_{AB} the current flowing around the loop is calculated as:

The voltage drop across 20 Ω resistor can be calculated

Vs = 20 – (20Ω x 0.33amp) = 13.33 volt.

Then the Thevenin’s equivalent circuit is shown below with 40Ω resistor connected.

The current flowing in the circuit is given as:

Thevenin’s theorem can be used as a circuit analysis method and is especially useful if the load is to take a series of different values. It is not as powerful as Mesh or Nodal analysis in larger networks because the use of Mesh or Nodal analysis is usually necessary for any Thevenin exercise, so it might well be used from the start. Thevenin’s equivalent circuit of Transistors, Voltage Sources are very useful in circuit design.

**Advantage Of Thevenin Theorem **

- It reduces a complex circuit to a simple circuit viz a single source of e.m.f. Eth in series with a single resistance RTh.
- It greatly simplifies the part of the circuit of the lesser importance and enables us to view the action of the output part directly.
- The theorem is especially useful to determine the current in a particular branch of a network as the resistance of that branch is varied while all other resistances and e.m.f source remain constant

## Some Question

**What are V _{TH} and R_{TH}?**

Thevenin voltage VTH is defined as the voltage across the load terminals when the load resistor is open. Because of this, the Thevenin voltage is sometimes called the open-circuit voltage (VTH= VOC).

Thevenin resistance is defined as the resistance that an ohmmeter measures across the load terminals of the figure above when all sources are reduced to zero and the load resistor is open (RTH = ROC).

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