A typical AA rechargeable battery has a voltage of 1.2 V and a rating of 1800 mA·h. How long could this battery drive current through a long, thin wire of 22 Ω resistance?

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Study for the UCF PHY2054 General Physics Exam. Use flashcards and multiple-choice questions complete with hints and explanations. Boost your understanding and get exam-ready!

Multiple Choice

A typical AA rechargeable battery has a voltage of 1.2 V and a rating of 1800 mA·h. How long could this battery drive current through a long, thin wire of 22 Ω resistance?

Explanation:
This question tests using battery capacity with a given load via Ohm’s law to find runtime. The battery’s rating of 1800 mAh means it can supply 1.8 Ah of charge under ideal conditions. The current through the 22 Ω wire at 1.2 V is I = V/R = 1.2/22 ≈ 0.0545 A (about 54.5 mA). The time you can run at that current is t = capacity / current = 1.8 Ah / 0.0545 A ≈ 33 h. So the battery could drive current for about 33 hours. In practice, voltage sag and internal resistance will reduce this a bit, but the ideal calculation gives the expected runtime.

This question tests using battery capacity with a given load via Ohm’s law to find runtime. The battery’s rating of 1800 mAh means it can supply 1.8 Ah of charge under ideal conditions. The current through the 22 Ω wire at 1.2 V is I = V/R = 1.2/22 ≈ 0.0545 A (about 54.5 mA). The time you can run at that current is t = capacity / current = 1.8 Ah / 0.0545 A ≈ 33 h. So the battery could drive current for about 33 hours. In practice, voltage sag and internal resistance will reduce this a bit, but the ideal calculation gives the expected runtime.

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