Network theorems and properties — match each theorem in List I with the corresponding network property or statement in List II. List I (Theorems) A. Reciprocity B. Tellegen's theorem C. Superposition D. Maximum power transfer List II (Property of network) 1. Impedance matching 2. Bilateral 3. Σ Vjk Ijk = 0 4. Linear

Introduction / Context:
This matching exercise checks conceptual understanding of four cornerstone network theorems and the kinds of networks or relationships they apply to. Knowing which theorem assumes linearity, bilaterality, or implies impedance-matching is essential for analysis and design in circuit theory, RF engineering, and signal processing.

Given Data / Assumptions:

• Networks are lumped and time-invariant unless stated otherwise.
• Independent sources can be turned off (for superposition) by replacing voltage sources with short circuits and current sources with open circuits.
• Tellegen's theorem is topological and applies broadly to networks obeying Kirchhoff's laws.
• Maximum power transfer is considered for resistive Thevenin equivalents driving a load.

Concept / Approach:

Map each theorem to its defining property: Reciprocity characterizes bilateral networks (responses are interchangeable between ports). Tellegen's theorem states the summation Σ Vjk Ijk = 0 across all branches in any network satisfying KCL and KVL. Superposition requires linearity to sum individual source effects. Maximum power transfer connects to impedance matching between source and load (in simple resistive cases, RL = RTh).

Step-by-Step Solution:

Verification / Alternative check:

Reciprocity tests interchange source and detector in a two-port and verify equal response. Tellegen's theorem holds for any choice of reference directions, confirming a universal power balance identity. Superposition fails in nonlinear networks (e.g., diodes). Maximum power transfer can be verified by differentiating load power with respect to RL and setting derivative to zero.

Why Other Options Are Wrong:

• Linking superposition to nonlinearity contradicts its requirement.
• Assigning reciprocity to matching confuses a property of port interchange with a design goal.
• Misplacing Tellegen's statement to linearity overlooks its topological basis.

Common Pitfalls:

Assuming reciprocity in active or strongly nonreciprocal media (e.g., ferrites under bias). Also, conflating maximum power transfer with maximum efficiency; matching maximizes load power, not efficiency.

Final Answer:

A-2, B-3, C-4, D-1