Source stiffness in circuit design: a 12 V source has internal resistance r_s = 0.5 Ω. For which load resistance values does this source behave “stiff” (i.e., minimal voltage sag under load)?

Introduction / Context:
A “stiff” voltage source maintains nearly constant terminal voltage when the load varies. Practically, this occurs when the load resistance is much larger than the source’s internal resistance, making load current small and IR drop inside the source negligible. This question checks whether you can apply the rule-of-thumb comparing R_load and r_s.

Given Data / Assumptions:

• Ideal source voltage: 12 V.
• Internal resistance r_s = 0.5 Ω.
• Goal: choose R_load values that cause minimal terminal voltage drop.

Concept / Approach:
Terminal voltage V_out = V_s * (R_load / (R_load + r_s)). If R_load >> r_s, then R_load / (R_load + r_s) ≈ 1 and V_out ≈ V_s. A common engineering heuristic is R_load ≥ 10 * r_s for “stiff” performance; higher ratios are even better. With r_s = 0.5 Ω, 10 * r_s = 5 Ω, which is the bare minimum threshold; substantially larger values like 50 Ω or 100 Ω produce very small sag and thus clearly “stiff” behavior.

Step-by-Step Solution:

Verification / Alternative check:
As a rule, R_load ≥ 10 * r_s is borderline; better stiffness with 100 * r_s. Both 50 Ω and 100 Ω satisfy >> 0.5 Ω; the inclusive choice “50 Ω or more” correctly captures the stiffness threshold among the options.

Why Other Options Are Wrong:

Common Pitfalls:
Forgetting internal resistance or assuming an ideal source. Always compare R_load to r_s to estimate voltage regulation quality.

Final Answer:
50 Ω or more