Thevenin’s Theorem

Thevenins Theorem
Figure: Thevenin's Equivalent Circuit



Thevenin’s Theorem

Thevenin’s theorem is suitable for linear bilateral network when it is desired to find the values of the current flowing through the resistor for its different values.  The solution of the complicated electrical networks are simplified by the thevenin’s theorem.

This theorem is a mathematical technique and replaces a complex electrical network into a simplified form consisting of a voltage source VT and resistance RT and RL as shown below.

Thevenins Theorem
Figure: Thevenin’s Equivalent Circuit

Here, VT is the Thevenin’s equivalent voltage, RT is the thevenin’s equivalent resistance and RL is the load resistance.

Where the current flowing into the load resistance in the Thevenin’s equivalent circuit is given by.

VT is the open-circuit voltage which appears across the load terminals when the load is removed from the network and RT is the equivalent resistance as seen inward from the load terminal when the source has been removed and replaced by its internal resistance.

Statement

For an electrical network, the current in any passive circuit element (such as a load resistance RL) will be same to that of a network in which the RL is supplied by a voltage source VT in series with equivalent resistance RT. Where VT is the open-circuit voltage which appears across the load terminals when the load is removed from the network and RT is the equivalent resistance as seen inward from the load terminal when the source has been removed and replaced by its internal resistance.

Application of Thevenin’s Theorem

Let us consider an electrical circuit as shown below.

Thevenin's Theorem
Figure: 1.1

Here ‘r’ is the internal resistance of the source EMF ‘E’. R1, R2 and RL are the resistances connected in the circuit.

RL is the load resistance where we want to determine the current using Thevenin’s theorem.

For the application of Thevenin’s theorem we have to determine the VT (Thevenin’s equivalent voltage) and RT (Thevenin’s equivalent resistance).

To determine the VT, we will remove the load resistance RL from the terminal AB and determine the open circuit voltage across it which will be the required VT.

Thevenins Theorem
Figure: 1.2

As, the R2 and the terminal AB is in parallel so the voltage across R2 is equal to the VT.

Then, current through R2 is

Therefore, voltage VT is

To determine RT, we will remove the source form the circuit leaving behind its internal resistance only and view the circuit inwards from the open terminal AB and determine the equivalent resistance. This equivalent resistance will be equal to the RT.

[If the internal resistance is negligible or not stated in the problem then replace the voltage source by short circuit and replace the current source by open circuit.]

Thevenins Theorem
Figure: 1.3

For this illustration, the equivalent resistance as seen inward from the terminal AB will be (r+R1)//R2.

Finally, the Thevenin’s equivalent circuit is formed. This is shown below.

Thevenins Theorem
Figure: 1.4

Where the load current IL is given by

Steps for Thevenin’s Theorem

The steps involved for analyzing a circuit or network using thevenin’s theorem is summarized in following points.

  1. Remove the load resistance RL (the resistance across which the current is to be determined) and determine the open circuit voltage across it. The open circuit voltage is equal to VT.
  2. Remove the source form the circuit leaving behind its internal resistance and determine the equivalent resistance RT of the circuit as seen inward form the load resistance RL. [If the internal resistance is negligible or not stated in the problem then replace the voltage source by short circuit and replace the current source by open circuit.]
  3. Draw the thevenin’s equivalent circuit and determine the current flowing in the circuit.

Examples

Here we will determine the current flowing through 2 Ohm resistor using thevenin’s theorem.

Thevenins Theorem
Figure: 2.1

At first, the 2 Ohm resistor is removed from the circuit and the open circuit voltage is calculated across the terminal AB as shown below.

Thevenins Theorem
Figure: 2.2

Now, the RT is calculated by replacing the source with its internal resistance. [As no internal resistance provided for the voltage source, so replace the source by short circuit].

Thevenins Theorem
Figure: 2.3

Now thevenin’s equivalent circuit is drawn.

Thevenins Theorem
Figure: 2.4

The current through 2 Ohm is given by.


RELATED POSTS:

NODAL ANALYSIS

MESH CURRENT ANALYSIS

KIRCHHOFF’S LAW

SUPEPOSITION THEOREM

MORE ON BASICS OF ELECTRICAL ENGINEERING. CLICK HERE.

MORE ON ELECTRICAL CIRCUIT THEORY. CLICK HERE.


ENGINEERING NOTES ONLINE: PID CONTROLLER

LEARN ELECTRICAL ENGINEERING

About Tanus Bikram Malla 46 Articles
Electrical Engineer

1 Trackback / Pingback

  1. Power System Structure | Engineering Notes Online

Leave a Reply

Your email address will not be published.


*