Thevenin equivalent form — which option correctly describes the standard Thevenin representation of any linear two-terminal network as seen from a pair of output terminals?

Introduction / Context:
Thevenin’s theorem is a powerful simplification tool. It allows you to replace any linear, bilateral two-terminal network with an equivalent source and resistance that behave identically from the perspective of the external load. Recognizing the correct canonical form is essential before you compute V_TH and R_TH.

Given Data / Assumptions:

• The original network is linear and bilateral (resistors, independent/dependent sources that are linear).
• We are looking from a specific pair of output terminals.
• Frequency effects are ignored unless reactive elements are converted to equivalent impedances (then R_TH becomes Z_TH).

Concept / Approach:
The Thevenin equivalent is defined as a single ideal voltage source V_TH in series with a single resistance R_TH (or impedance Z_TH). V_TH equals the open-circuit voltage at the terminals. R_TH equals the equivalent resistance seen looking back into the network with independent sources deactivated (voltage sources shorted, current sources opened), or equivalently the ratio of V_TH to I_SC for purely resistive linear circuits.

Step-by-Step Solution:

Verification / Alternative check:
Confirm equivalence by checking that, for any RL, the original network and the Thevenin model produce identical terminal voltage and current.

Why Other Options Are Wrong:

Common Pitfalls:
Mixing up Norton and Thevenin forms; forgetting to deactivate sources properly when finding R_TH; applying the theorem to nonlinear networks.

Final Answer:
A voltage source in series with a resistance