# 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 1. Remove the portion of the network across which the Thevenin’s Equivalent circuit is to be found.

2.Mark the terminal AB of the remaining 2 terminal circuit.

3.Obtain the open circuit voltage at the terminal AB i.e Vth keeping all the sources at their normal values. 4. 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   5.Draw the equivalent circuit across AB,  Thevenin’s voltage Vth in series with Zth.  ## Application of Thevenin’s Theorems

• Replaces the large part of a network i.e complicated and uninteresting part by a very simple equivalent.
• Helps in the rapid calculation of the voltage ,current and hence power which the original circuit is able to deliver to a load.
• Helps to choose the best value of load resistance or impedance required to accomplish a maximum transfer of power.

## Limitations of Thevenin’s Theorems

• It is not applicable to the circuits consisting of unilateral elements like diode etc.
• Not applicable for the circuits consisting of non-linear elements like diode ,transistor etc.
• Not applicable for the circuits consisting of load series or parallel with controlled or dependent sources.
• Not applicable to the circuits consisting of magnetic coupling between load and any other circuit element.