Battery capacity interpretation: A power supply can deliver 6 A continuously for 3.5 h. What is its ampere-hour (Ah) rating under these conditions?

Introduction / Context:
Ampere-hour (Ah) rating expresses how much charge a source can deliver over time. It is widely used for batteries and backup supplies. Translating current and runtime into Ah is straightforward but must be done carefully.

Given Data / Assumptions:

• Current capability I = 6 A (assumed constant).
• Duration t = 3.5 h.
• Assume ideal conditions with negligible rate effects or temperature derating.

Concept / Approach:

Ampere-hours = current (A) * time (h). This is effectively the total charge delivered, since 1 Ah = 3600 coulombs. While real batteries vary with discharge rate, the arithmetic remains the basic rating method.

Step-by-Step Solution:

Verification / Alternative check:

In coulombs: Q = I * t = 6 * 3.5 * 3600 ≈ 75,600 C. Convert back: 75,600 C / 3600 ≈ 21 Ah, confirming the result.

Why Other Options Are Wrong:

58 Ah or 35 Ah do not match the simple product. 2.1 Ah and 0.58 Ah are off by factors of 10 or more.

Common Pitfalls:

Confusing Ah (capacity) with Wh (energy), which would also require voltage. Misreading hours (e.g., minutes) can lead to large errors.

Final Answer:

21 Ah