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**Statement of Thevenin’s Theorem**

Any permutation of linear bilateral circuit elements and active sources, apart from the connections or complication, connected to a certain load R

_{L}possibly will replace by a simple two terminal network consisting of a single voltage source of V_{m}volts and a single resistance R_{eq}in series with the voltage source, across the two terminals of the resistance load R_{L}. The voltage V_{TH}is the open circuit voltage measured at the two terminals of interest, with load resistance R_{L}removed. This voltage is known as Thevenin's equivalent voltage. The R_{eq}is the equivalent resistance of the given network as viewed through the terminals where R_{L}is connected, but with R_{L}removed and all the active sources are replaced by their internal resistances.###
**Explanation of Thevenin's Theorem**

The theory of Thevenin's equivalent across the terminals of interest can be explained by considering the circuit shown in the Fig-a. The terminals A-B are the terminals of interest across which R

_{L}is connected. Then Thevenin's equivalent across the load terminals A-B can be obtained as shown in the Fig-b.

The voltage V

_{TH}is obtained across the terminals A-B with R_{L}removed. Hence V_{TH}is also called open circuit Thevenin's voltage. The circuit to be used to calculate V_{TH}is shown in the Fig-a, for the network considered above. While R_{eq}is the equivalent resistance obtained as viewed through the terminals A-B with R_{L}removed, voltage sources replaced by short circuit and current sources by open circuit. This is shown on the fig - b.While obtaining V

_{TH}, any of the network simplification techniques can be used. When the circuit is replaced by Thevenin's equivalent across the load resistance, then the load current can be obtained as

**I**

_{L}= V_{TH}/(R_{L}+ R_{eq}).By using this theorem, current through any branch of the circuit can be obtained, treating that branch resistance as the load resistance and obtaining Thevenin's equivalent across the two terminals of that branch resistance as the load resistance and obtaining Thevenins equivalent across the two terminals of the branch.

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__Steps to Apply Thevenin's Theorem__

- Remove the branch resistance through which current is to be calculated.
- Calculate the voltage across these open circuited terminals, by using any of the network simplification techniques. This is V
_{TH}. - Calculate R
_{eq}as viewed through the two terminals of the branch from which current is to be calculated by removing that branch resistance and replacing all independent sources by their internal resistances. If the internal resistances are not known then replace Independent voltage sources by short circuits and independent current sources by open circuits. - Draw the Thevenin's equivalent showing source V
_{TH}, with the resistance R_{eq}in series with it, across the terminals of branch of interest. - Reconnect the branch resistance. Let it be R
_{L}. The required current through the branch is given by,

**I = V**

_{TH}/ (R_{eq}+ R_{L})####
__Limitations of Thevenin's Theorem:__

The limitations of Thevenin's theorem are;

- Not applicable to the circuits consisting of nonlinear elements.
- Not applicable to unilateral networks.
- There should not be magnetic coupling between the load and circuit to be replaced by Thevenin's theorem.
- In the load side, there should not be controlled sources, controlled from some other part of the circuit.