For procedures, see your electrical laboratory manual.

Title: Verification of some network theorem

1. Superposition Theorem
2. Thevenin's Theorem


Apparatus

1. 2 DC Power Supply
2. 4 Decade Resistance Boxes
3. An AVO Meter


First Method - Superposition Theorem

Aim

To verify Superposition Theorem using a resistance circuit.

Theory

The superposition theorem is based on the concept of linearity between the response and excitation of an electrical circuit. It states that the response in a particular branch of a linear circuit when multiple independent sources are acting at the same time is equivalent to the sum of the responses due to each independent source acting at a time.

This theorem also states that "in a linear network, the output responses (i.e. voltage or current values) due to a number of sources (i.e. voltage and/or current sources) acting simultaneously is simply the algebraic sum of the responses which would be produced by each of the sources acting alone with all the other sources dead".


The superposition theorem is used to solve the network where two or more sources are present and connected.


Suppose an electrical circuit having several branches and or loads and also several sources some being current source and some being voltage source. Then Superposition theorem suggests that:
If we find the branch responses (Voltage drop and Current through it) on a branch due to only of those sources by ignoring the effect of all other sources or replacing all other sources by their corresponding internal impedance and repeat the process for every source on the circuit. Then the Combined responses (Voltage drop and Current through it) on a branch due to all the sources combined is the algebraic sum of responses on the branches due to each individual source.

Second Method - Thevenin's Theorem

Aim

To verify Thevenin's Theorem using a resistance circuit.

Theory

Thevenin’s Theorem states that – any complicated network across its load terminals can be substituted by a voltage source with one resistance in series. This theorem helps in the study of the variation of current in a particular branch when the resistance of the branch is varied while the remaining network remains the same for example designing of electronics circuits.

A more general statement of Thevenin’s Theorem is that any linear active network consisting of independent or dependent voltage and current source and the network elements can be replaced by an equivalent circuit having a voltage source in series with a resistance, that voltage source being the open-circuited voltage across the open-circuited load terminals and the resistance is the internal resistance of the source.

In other words, the current flowing through a resistor connected across any two terminals of a network by an equivalent circuit having a voltage source Eth in series with a resistor Rth. Where Eth is the open-circuit voltage between the required two terminals called the Thevenin voltage and the Rth is the equivalent resistance of the network as seen from the two-terminal with all other sources replaced by their internal resistances called Thevenin resistance.


This theorem is possibly the most extensively used network theorem. It is applicable where it is desired to determine the current through or voltage across any one element in a network. Thevenin’s Theorem is an easy way to solve a complicated network.


Thevenin’s theorem can be used as a circuit analysis method and is particularly useful if the load is to take a series of different values. It is not as powerful as Mesh or Nodal analysis in larger networks because the use of Mesh or Nodal analysis is usually necessary for any Thevenin exercise, so it might well be used from the start. However, Thevenin’s equivalent circuits of Transistors, Voltage Sources such as batteries, etc, are very useful in circuit design.