Design guideline for a “stiff” current source: If a current source has an internal resistance of 100 kΩ (in parallel with the source), what is the largest load resistance you would choose so the source still appears stiff?

Introduction / Context:A practical current source is modeled as an ideal current source in parallel with a large internal resistance R_int. To appear “stiff,” the load current should be close to the ideal source value and not vary much with changes in load. Choosing an appropriate load resistance is key.

Given Data / Assumptions:

• Internal (parallel) resistance R_int = 100 kΩ.
• Stiffness rule of thumb: R_int should be at least about 10 times greater than R_load.
• We seek the largest R_load still meeting that guidance.

Concept / Approach:With an ideal current source I_S in parallel with R_int feeding R_load, current division gives I_load = I_S * (R_int / (R_int + R_load)). To keep I_load ≈ I_S, require R_int ≫ R_load. A common heuristic is R_int ≥ 10 * R_load (error <≈ 10%).

Step-by-Step Solution:Apply heuristic: R_load ≤ R_int / 10.Compute: R_int / 10 = 100 kΩ / 10 = 10 kΩ.Therefore, the largest advisable load is about 10 kΩ.

Verification / Alternative check:Exact division: I_load/I_S = 100k / (100k + 10k) ≈ 0.909, about 9% error—typical stiffness target for preliminary design.

Why Other Options Are Wrong:20 kΩ: ratio only 5:1; larger error (~17%).2 kΩ or 1 kΩ: these are acceptable (even stiffer), but the question asks for the largest value that still qualifies; 10 kΩ is larger.None: incorrect since 10 kΩ fits the design rule.

Common Pitfalls:Using series-source intuition (for voltage sources) instead of parallel model; forgetting that “stiff” for current sources means small load compared with internal resistance.

Final Answer:10 k Ohm