Understanding Network Theorems

Network theorems are powerful tools used in circuit analysis to simplify complex electrical networks. They allow us to analyze circuits more easily by replacing parts of the network with simpler equivalent circuits. Key theorems include Thevenin's theorem, Norton's theorem, and concepts like source transformation and mesh analysis.

Analyzing the Statements

Let's examine each statement provided in the options to determine which one is true.

Analyzing Statement 1: Source Transformation and Thevenin/Norton Theorems

The first statement says: Source transformation of Thevenin theorem is known as Norton theorem.

Source transformation is a technique used to convert a voltage source in series with a resistance into an equivalent current source in parallel with the same resistance, and vice versa. This technique is precisely the method used to relate Thevenin's equivalent circuit (a voltage source in series with a resistance) to Norton's equivalent circuit (a current source in parallel with the same resistance).

A Thevenin equivalent circuit consists of an ideal voltage source (\(V_{Th}\)) in series with a Thevenin resistance (\(R_{Th}\)).

A Norton equivalent circuit consists of an ideal current source (\(I_N\)) in parallel with a Norton resistance (\(R_N\)).

Source transformation shows that these two forms are equivalent, where \(I_N = V_{Th} / R_{Th}\) and \(R_N = R_{Th}\). Therefore, the process of converting between the Thevenin and Norton equivalents is achieved through source transformation. While it's not that source transformation *is* the Norton theorem itself, it is the direct relationship and conversion method *between* the Thevenin and Norton theorems/equivalent circuits.

This statement is essentially describing the relationship between Thevenin and Norton theorems via source transformation.

Analyzing Statement 2: Norton Equivalent Circuit

The second statement says: Any two terminals of a network can be replaced by an equivalent voltage and equivalent series resistance in Norton theorem.

This statement describes the Thevenin theorem, not the Norton theorem. Norton's theorem states that any linear two-terminal network can be replaced by an equivalent circuit consisting of a current source (\(I_N\)) in parallel with a resistance (\(R_N\)). The statement incorrectly uses "equivalent voltage and equivalent series resistance," which belongs to Thevenin's theorem.

Therefore, this statement is false.

Analyzing Statement 3: Source Replacement in Thevenin Theorem

The third statement says: In Thevenin theorem, the voltage source is replaced by an open circuit and the current source is replaced by a short circuit.

This statement describes the procedure for finding the Thevenin equivalent resistance (\(R_{Th}\)). When calculating \(R_{Th}\) for a network containing independent sources, independent voltage sources are replaced by short circuits (zero voltage) and independent current sources are replaced by open circuits (zero current). The statement mixes up which source is replaced by which type of circuit element.

• Voltage source replaced by short circuit.
• Current source replaced by open circuit.

The statement reverses the replacements. Therefore, this statement is false.

Analyzing Statement 4: Definition of Super Mesh

The fourth statement says: The super mesh is defined as the combination of two meshes that have voltage source at their boundaries.

A super mesh is formed when a current source (either independent or dependent) exists between two meshes that do not have a series element in common with the current source. It is the presence of a *current source*, not a voltage source, on the boundary between two meshes that defines a super mesh.

Therefore, this statement is false.

Conclusion

Based on the analysis of each statement:

• Statement 1 is true because source transformation is the fundamental technique connecting the Thevenin and Norton equivalent circuits.
• Statement 2 is false as it describes the Thevenin equivalent, not Norton.
• Statement 3 is false as it incorrectly describes how sources are handled when finding equivalent resistance.
• Statement 4 is false as a super mesh is formed by a current source between meshes, not a voltage source.

Thus, the only true statement is the first one.