Network equivalence theorems: Which theorem allows replacing a linear, bilateral two-terminal network with an equivalent circuit consisting of a single voltage source in series with a single resistance?

Introduction / Context:
Equivalence theorems simplify complex networks into basic source–resistance models that are easier to analyze, especially when studying the effect of varying loads. Recognizing whether to use Thevenin or Norton form is a staple skill in circuit theory and lab measurement practice.

Given Data / Assumptions:

• Network is linear and bilateral (resistors, independent/dependent sources, and linear elements).
• Two-terminal view toward the load.
• Goal: replace with a simple, functionally equivalent source–resistance pair.

Concept / Approach:
Thevenin’s theorem states any linear two-terminal network can be replaced by an equivalent voltage source V_th in series with a resistance R_th as seen from the load terminals. Norton’s theorem is the dual form using a current source I_no in parallel with R_no, where V_th = I_no * R_th and R_th = R_no. Superposition is a technique for analyzing circuits with multiple sources; it is not an equivalence replacement. “Multinetwork” is not a standard theorem.

Step-by-Step Solution:
Find V_th: compute open-circuit voltage at the terminals.Find R_th: zero independent sources (voltage sources → short, current sources → open) and compute equivalent resistance seen from the terminals.Form the Thevenin equivalent: a single ideal voltage source V_th in series with R_th.Connect the load to analyze currents/voltages easily.

Verification / Alternative check:
Convert between Thevenin and Norton: I_no = V_th / R_th and R_no = R_th. Solving a sample network both ways yields identical load behavior, confirming equivalence.

Why Other Options Are Wrong:
Norton: equivalent current source with parallel resistance, not a series resistance with a voltage source.Superposition: analysis method, not a replacement theorem.Multinetwork: not a recognized theorem in basic circuit theory.

Common Pitfalls:
Confusing how to compute R_th in the presence of dependent sources (a test source is then required). Always apply the correct procedures for networks with dependent elements.

Final Answer:
Thevenin