A battery is rated at 80 ampere-hours. (a) What does the unit ampere-hour measure? (b) How many coulombs of charge can it deliver?

What the rating is telling you

A battery “ampere-hour” rating is a capacity rating. It tells you how much total charge the battery can supply, not the voltage and not the energy directly.

(a) Meaning of the unit ampere-hour

Current is charge per time: $$I = \frac{Q}{t}$$ Rearranging gives: $$Q = It$$ So the unit $\text{A}\cdot\text{h}$ (ampere-hour) is a unit of charge.

(b) Converting $80\,\text{Ah}$ to coulombs

Use the fact that:

• $1\,\text{A} = 1\,\text{C/s}$
• $1\,\text{h} = 3600\,\text{s}$

So: $$1\,\text{Ah} = (1\,\text{C/s})(3600\,\text{s}) = 3600\,\text{C}$$ Now multiply by 80: $$Q = 80\,\text{Ah}\times 3600\,\text{C/Ah} = 288000\,\text{C} = 2.88\times 10^5\,\text{C}$$

Quick interpretation check

If the battery delivered $80\,\text{A}$ for $1\,\text{h}$, the charge delivered would be $Q = It = 80\times 3600\,\text{C}$, which matches the calculation.