# Thevenin’s Theorem: Calculation, Application, Limitation

The application of Thevenin’s theorem enables the simplification of a linear circuit to its Thevenin equivalent circuit, which comprises a solitary voltage source and a series resistance. This simplification can facilitate the assessment of the impacts resulting from modifications in the connected load.

## What is Thevenin’s theorem?

Thevenin’s theorem states that,” With respect to terminal pair AB, the network N may be replaced by a voltage source Vth in series with an internal impedance Rth.

The voltage source Vth called the Thevenin’s voltage is the potential difference (VA-VB) between the terminal A & B, Rth is the internal impedance of the network N as seen from the terminals A&B with all the sources set to Zero i.e. with all the voltage sources shorted and all the current sources open circuited leaving behind their internal resistance and impedances.”

The series combination of Vth and Rth is known as Thevenin’s equivalent of the network N with respect to terminal pair AB. Consider an active linear network N, represented by a black box. Let A&B be any pair of terminals of N with respect to which an equivalent circuit is desired.

Hence ,if a load impedance RL be connected across terminal A & B of network N ,the current IL delivered to the load may be calculated from the equivalent circuits by connecting this impedance across A&B and shall be given as

## Procedure to Obtain Vth and Rth

• Remove the portion of the network across which the Thevenin’s Equivalent circuit is to be found.
• Mark the terminal AB of the remaining 2 terminal circuit.
• Obtain the open circuit voltage at the terminal AB i.e Vth keeping all the sources at their normal values.
• Calculate Rth.

## For the calculation of Thevenin’s Resistance

case I:

If circuit having only independent sources. In this case, set all the sources at Zero values i.e with all the voltage sources shorted and all the current sources open circuited leaving behind their internal resistances or impedances.

case II:

If circuit having independent and dependent sources both: In this case, we calculated Vth ,then the internal impedance of the network N is obtained as Rth.

case III:

If circuit having only dependent sources: In this case , we apply a voltage V at the terminal pair AB.A current I will flow due to application of V , then the internal impedance of the network N is obtained as

• Draw the equivalent circuit across AB,  Thevenin’s voltage Vth in series with Zth.