Question

A battery with a \(12\,\text{V}\) emf has an initial charge of \(80\,\text{A·h}\). If the potential across the terminals remains constant until it is fully discharged, how long can the battery deliver energy at a rate of \(120\,\text{W}\)?

• A. \(16\, \text{h}\)
• B. \(8\, \text{h}\)
• C. \(4\, \text{h}\)
• D. \(5\, \text{h}\)

Hint:

Use \( E = VQ \) and \( P = \frac{E}{t} \). Convert ampere-hours to coulombs for total charge: \( 1 \, \text{A·h} = 3600 \, \text{C} \).

Answer 1

The Correct Option is B

Energy stored in the battery: \[ Q = 80 \, \text{A·h} = 80 \times 3600 = 288000 \, \text{C} \] Total energy: \[ E = V \cdot Q = 12 \cdot 288000 = 3456000 \, \text{J} \] Power delivered: \[ P = 120 \, \text{W} \Rightarrow t = \frac{E}{P} = \frac{3456000}{120} = 28800 \, \text{s} = \frac{28800}{3600} = 8 \, \text{hours} \]