Thevenin–Norton equivalence: The Thevenin resistance seen at a circuit’s output terminals is equal to what quantity?

Introduction / Context:
Thevenin’s theorem simplifies a linear network to a voltage source in series with a resistance as seen by a load. Correctly identifying the Thevenin resistance is essential for matching, maximum power transfer analysis, and quick hand calculations.

Given Data / Assumptions:

• Circuit is linear and time-invariant around the operating point.
• Independent sources may be present (voltage or current).
• We examine the resistance “seen” at the load terminals.

Concept / Approach:
The Thevenin resistance R_th equals the input resistance looking back into the network with all independent sources turned off (voltage sources replaced by their internal resistances, ideal ones shorted; current sources opened). This resistance also equals the Norton resistance R_no for the Norton equivalent, since the two models are duals.

Step-by-Step Solution:
Remove the load to expose the output terminals.Turn off all independent sources (short ideal voltage sources, open ideal current sources).Calculate the equivalent resistance seen into the network; this is R_th.Note: Dependent sources remain active; use a test source method if needed.

Verification / Alternative check:
Compute open-circuit voltage V_oc and short-circuit current I_sc. Then R_th = V_oc / I_sc, which must match the resistance obtained with sources turned off.

Why Other Options Are Wrong:
Load resistance / half load: R_th is a property of the source network, not the attached load.Open-load resistance of the load: unrelated; concerns the load device, not the network.None: incorrect because the standard definition is provided.

Common Pitfalls:
Turning off dependent sources (do not); forgetting to account for internal source resistances; mixing up R_th with matched load conditions.

Final Answer:
The equivalent resistance seen at the output terminals with all independent sources turned off (same as Norton resistance)