Stiff source rule-of-thumb (1% regulation criterion): a 15 V source has internal resistance Rs = 0.2 Ω. Which load resistance is the smallest that still qualifies the source as “stiff” under the 1% rule (Rs ≤ 0.01 * RL)?
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A20 Ohm
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B30 Ohm
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C10 Ohm
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D100 Ohm
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ENone of the above
Answer
Correct Answer: 20 Ohm
Explanation
Introduction / Context:A voltage source is considered “stiff” if its terminal voltage changes very little when the load varies. A common engineering rule uses a ratio between source resistance and load resistance to quickly judge stiffness and expected regulation without a full analysis.
Given Data / Assumptions:
- Ideal source voltage Vs = 15 V (magnitude does not affect the ratio test).
- Internal (source) resistance Rs = 0.2 Ω.
- Stiffness rule-of-thumb: Rs ≤ 0.01 * RL (approximately 1% regulation).
Concept / Approach:Using the voltage divider model, Vout = Vs * RL / (Rs + RL). If Rs is much smaller than RL, Vout ≈ Vs with minimal drop. The 1% rule requires Rs to be at most 1% of RL, i.e., RL ≥ 100 * Rs. For a given Rs, we compute the minimum RL that satisfies the criterion and select that from the options.
Step-by-Step Solution:
1) Apply criterion: RL ≥ 100 * Rs.2) Substitute Rs = 0.2 Ω → RL ≥ 100 * 0.2 = 20 Ω.3) Among the options, 20 Ω is the smallest value meeting the rule; larger values (30 Ω, 100 Ω) also qualify but are not the smallest qualifying load.Verification / Alternative check:Compute regulation at RL = 20 Ω: Vout = 15 * 20 / (0.2 + 20) ≈ 15 * 20 / 20.2 ≈ 14.85 V (about 1% drop), confirming stiffness at the threshold.
Why Other Options Are Wrong:
10 Ω: Fails the 1% rule because Rs would be 2% of RL.30 Ω and 100 Ω: They are acceptable but not the smallest that still qualifies under the stated rule.None of the above: Incorrect because 20 Ω meets the criterion exactly.Common Pitfalls:Ignoring that the question asks for the minimum qualifying value; mixing absolute numbers with ratio-based criteria; forgetting that Vs magnitude does not change the ratio test.
Final Answer:20 Ohm.