Source modeling: for an approximately ideal (stiff) current source driving a load of 1 kΩ, what range of internal source resistance best maintains constant current through the load?

Introduction / Context:
A practical current source is modeled as an ideal current source in parallel with a large internal resistance (or as a Thevenin equivalent with very high output resistance). A source is called stiff when its output current changes very little as the load varies. This question connects the concept to numerical ranges relative to a 1 kΩ load.

Given Data / Assumptions:

• Load resistance R_L = 1 kΩ.
• We desire a stiff current source, meaning output resistance R_s much greater than R_L.
• Rule of thumb: R_s should be at least 100 times R_L for strong stiffness.

Concept / Approach:
For a current source, output resistance should be very high so that load changes produce minimal current deviation. If R_s ≥ 100 * R_L, the current variation with load is typically small. With R_L = 1 kΩ, this suggests R_s ≥ 100 kΩ.

Step-by-Step Solution:
Step 1: Identify stiffness condition: R_s >> R_L.Step 2: Apply the 100 times guideline: R_s ≥ 100 * 1 kΩ = 100 kΩ.Step 3: Select the option that ensures R_s exceeds 100 kΩ.

Verification / Alternative check:
Small-signal output resistance analysis shows that larger R_s reduces the slope of the I–V curve, keeping current nearly constant for load changes. Simulation with R_s values above 100 kΩ confirms minimal current variation for a 1 kΩ load.

Why Other Options Are Wrong:

• At least 10 Ohm / Less than 10 Ohm: Far too small; would make a voltage-like source, not a current-like source.
• Less than 100 k Ohm: Not sufficiently high relative to 1 kΩ for stiffness.
• None of the above: Incorrect because more than 100 kΩ is appropriate.

Common Pitfalls:
Confusing source stiffness rules between voltage and current sources. Voltage sources should have low internal resistance; current sources should have high internal resistance.

Final Answer:
More than 100 k Ohm.