A flashlight battery has an internal resistance of 1 Ω. For what range of load resistance will the source effectively behave as a stiff (low-drop) voltage source?

Introduction / Context:A real battery has an internal resistance r that causes a voltage drop under load. A source is called 'stiff' if its terminal voltage hardly sags when the load current changes. This question checks whether you can relate the stiffness idea to the ratio of load resistance RL to internal resistance r.

Given Data / Assumptions:

• Internal resistance r = 1 Ω.
• We want RL values for which the terminal voltage is close to the ideal emf.
• Assume a simple Thevenin model: source E in series with r feeding RL.

Concept / Approach:

• Voltage division: Vout = E * RL / (r + RL).
• Stiff source criterion (rule-of-thumb): RL ≥ 10 * r keeps drop across r ≤ ~10% of E.
• Larger RL relative to r → smaller current → smaller Ir drop in r.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 60 Ω and 50 Ω: Better than 10r, but '100 Ω or more' is the most clearly stiff region offered.
• 10 Ω: Barely at the 10r edge; still ~9% drop, not strongly 'stiff'.
• None of the above: Incorrect because 100 Ω or more is suitable.

Common Pitfalls:

• Confusing maximum power transfer (RL = r) with stiffness; RL = r gives 50% voltage drop, not stiff.
• Ignoring that 'stiff' is about small percentage sag, not absolute resistance values.

Final Answer: