Network theorems and hallmark properties: Match each theorem to the most distinguished property it leverages. List I (Theorem) List II (Property) A. Reciprocity 1. Impedance matching B. Tellegen’s 2. Bilateral behavior C. Superposition 3. Σ v_k i_k = 0 power balance form (network identity) D. Maximum power transfer 4. Linearity (responses add)
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AA-1, B-2, C-3, D-4
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BA-1, B-2, C-3, D-5
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CA-2, B-3, C-4, D-1
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DA-2, B-3, C-5, D-1
Answer
Correct Answer: A-2, B-3, C-4, D-1
Explanation
Introduction / Context:Each classic network theorem highlights a structural property of circuits. Correctly pairing them helps in quickly selecting which theorem applies in analysis or design.
Given Data / Assumptions:
- Linear, time-invariant circuit assumptions for superposition and reciprocity.
- Tellegen’s theorem is topology-based and universally valid.
- Maximum power transfer refers to source/load impedance relation.
Concept / Approach:
Map the theorem to the property it fundamentally uses: reciprocity ↔ bilateral networks, Tellegen ↔ power balance identity, superposition ↔ linearity, and maximum power transfer ↔ impedance matching.
Step-by-Step Solution:
Reciprocity → bilateral behavior ⇒ A-2.Tellegen’s → Σ v_k i_k = 0 style identity ⇒ B-3.Superposition → linearity requirement ⇒ C-4.Max power transfer → impedance matching between source and load ⇒ D-1.Verification / Alternative check:
Text derivations show reciprocity matrices symmetric only for bilateral linear networks; Tellegen’s holds for any lumped network; superposition fails for nonlinear elements; maximum power occurs when load equals Thevenin impedance (or its conjugate in AC).
Why Other Options Are Wrong:
- Pairing superposition with “non-linear” contradicts its premise.
- Associating reciprocity with matching confuses a property with a design criterion.
Common Pitfalls:
Thinking Tellegen’s requires linearity; it does not—it is topology-based and widely valid.
Final Answer:
A-2, B-3, C-4, D-1