Thevenin equivalence — the Thevenin equivalent voltage seen at a pair of terminals equals the open-circuit voltage measured at those terminals. Is this statement accurate for linear networks?

Introduction / Context:
Thevenin’s theorem lets you replace a complicated linear network with a single ideal voltage source in series with a resistance as seen from two terminals. The core quantity is the Thevenin voltage, which many learners confuse. This question asks whether V_th equals the open-circuit voltage at the terminals.

Given Data / Assumptions:

• Linear, bilateral elements (resistors, sources; reactive elements permitted at a fixed frequency for phasors).
• No load attached when measuring open-circuit voltage.
• The network is observed from a specified port (two terminals).

Concept / Approach:
By definition, the Thevenin voltage V_th is the terminal voltage when the output is open-circuited (no load current). With no load current, internal drops through the Thevenin resistance are zero, so the terminal voltage equals the ideal source voltage in the Thevenin model. Therefore, V_th = V_open-circuit is not merely a rule of thumb but the formal definition in Thevenin analysis.

Step-by-Step Solution:

Verification / Alternative check:
Build a resistive divider: with the output open, the node voltage is V_oc from the divider equation. In the Thevenin model, the same node is driven by V_th in series with R_th; with I_load = 0, drops across R_th are zero, so the terminal voltage equals V_th, matching V_oc.

Why Other Options Are Wrong:

• Incorrect: Conflicts with the definition of Thevenin voltage.
• Only resistive: The statement also holds for reactive networks at a given frequency (phasor steady state).
• Only when a load is connected: This reverses the concept; V_th is defined with no load connected.

Common Pitfalls:
Confusing V_th with the loaded output; forgetting that R_th affects the voltage only when load current flows; mixing Norton parameters with Thevenin parameters.

Final Answer:
Correct — V_th equals the open-circuit terminal voltage.