# Thevenin's Theorem

### Statement/Definition:-

Thevenin’s theorem states that a linear and bilateral network can be replaced by an equivalent circuit consisting of a voltage source Vth in series with a resistance Rth.
In any linear bilateral network having more than one element, it can be replaced by a single equivalent circuit consisting of an equivalent voltage source (Vth) in series with equivalent resistance (Rth).

### Circuit Diagram:-

Thevenin’s equivalent circuit resembles a practical voltage source. Hence, it has a voltage source in series with a resistance.
• The voltage source present in the Thevenin’s equivalent circuit is called as Thevenin’s equivalent voltage or Thevenin’s voltage, Vth.
• The resistor present in the Thevenin’s equivalent circuit is called as Thevenin’s equivalent resistor or simply Thevenin’s resistance Rth.

### Step By Step Procedure:-

Thevenin theorem is a procedure by which we change a complex network (or circuit) into a simple network called Thevenin's equivalent circuit.
Thevenin’s equivalent circuit of an open-circuit voltage or Thevenin voltage(Vth) and the total resistance from the side of the open terminal, Thevenin's equivalent resistance (Rth). Connected both thevenin's quantities in series. In this way, we can find the current or voltage of any branch of the circuit (or network).

#### STEP 1:-

Remove that resistance in which current is wanted like RL.

#### STEP 2:-

Find the open-circuit voltage, VAB called Thevenin's equivalent voltage (Vth).

#### STEP 3:-

Find the total resistance, from open terminals A and B side, is called Thevenin's equivalent resistance (Rth) removing actual voltage source from the circuit.

#### STEP 4:-

Connect Vth and Rth in series. This will be the Thevenin's equivalent circuit.

#### STEP 5:-

Reconnect the RL (load resistance) between the open terminals of the Thevenin's equivalent circuit.

#### STEP 6:-

Find the current in RL( load resistance).

As both resistances are connected in series so the current in RL and Rth are the same.

### Example/Problem and Calculation:-

#1.

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• Thevenin's theorem is very useful in linear network analysis because by using Thevenin's theorem a large part of a network, often a complicated and uninteresting part can be replaced by a very simple equivalent circuit that enables us to make rapid calculations.
• It is very useful when it is desired to determine the current through or voltage across any one element in a network instead of going through the lengthy method of solving the network.
• It reduces a complex circuit into a simple circuit viz a single source of e.m.f. Eth in series with a single resistance RTh.
• It greatly simplifies the portion of a circuit of the lesser importance and enables us to view the action of the output part directly.
• This theorem is particularly useful to find current in a particular branch of the network as the resistance of that branch is varied while all other resistances and e.m.f (voltage)source remain constant.

• It is applicable only for linear and bilateral networks. for nonlinear and unilateral networks this theorem is not applicable. Some times power dissipation also not the same as a real circuit.
• It assumes that the circuit is completely linear. So, this theorem is applicable for resistors (resistances), but will not work well when trying to analyze circuits consisting of non-linear elements such as diodes.
• Actually, most of the circuits behave like a linear circuit in a certain range of values, thus this theorem is valid only within this linear range.
• Thevenin theorem is applicable only for bilateral networks, that is, for those networks where the current through the element is not affected with polarity changing.
• There should not be any magnetic coupling present in between a load & the network.
• The power dissipation by the Thevenin equivalent circuit is not always identical to the power dissipation by the real circuit. This particular limitation may lead to disturbances in proper circuit analysis.

### Application:-

To determine Change in Load Voltage, To predict the range of load voltage variation due to change in load resistance.
• To obtain Norton’s equivalent circuit.
• To determine Maximum power that can be transferred to Load from the network.
• It is useful for the electrical calculation of the circuits.
• It is used in transmission line drive calculation.
• The interesting way to simplify the circuit diagram allowing to search a partial solution in the selected zone to be analyzed.

### Conclusion:-

Thevenin Theorem is a basic equivalence principle for circuit design. It can simplify a very complex circuit into a very simple equivalent. This is done by finding the Thevenin Resistance (Rth) as well as the Thevenin voltage (Vth) and current. Once they are known, the equivalent circuit (or network) is simply a voltage source in series with a resistance.

• Thevenin’s Theorem is a way to reduce a network to the equivalent circuit (or network) composed of a single voltage source, series resistance, and series load.

#### • Steps to follow for Thevenin’s Theorem:-

• Find the Thevenin source voltage by removing the load resistance (RL) from the original circuit and calculating the voltage across the open connection points where the load resistor used to be.
• Find the Thevenin resistance (Rth) by removing all power sources in the original circuit (voltage sources shorted (S.C) and current sources open(O.C)) and calculating total resistance between the open connection points.
• Draw the Thevenin equivalent circuit, with the Thevenin voltage source (Vth) in series with the Thevenin resistance( Rth). The load resistance (RL) re-attaches between the two open points of the equivalent circuit.
• Analyze voltage and current for the load resistance (RL) following the rules for series circuits.

### Reference:-

• Circuit Theory: Analysis & Synthesis, Author’s Name: Abhijit Chakrabarti
• Fundamentals of Electric Circuits by Charles K. Alexander, Matthew N. O. Sadiku
•  Network Analysis by Van Valkenburg.
• Wikipedia, etc.

### Buy Below Books/Ebooks for More knowledge and Solving Questions:-

Thevenin Theorem - Statement | Circuit Diagram | Procedure | Advantages | Disadvantage | Application | Conclusion Reviewed by Siddharth on October 29, 2019 Rating: 5

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