Energy stored in a battery

Question: My old camcorder runs off of a big lead-acid battery that is labeled 12 volts, 4 AH. The "AH" stands for ampere-hours. What is the maximum amount of energy the battery can store?

Solution: An ampere-hour is a unit of current multiplied by a unit of time. Current is charge per unit time, so an ampere-hour is in fact a funny unit of charge:

(4 A)(1 hour) = (4 C/s)(3600 s)

= 14400 C

Now 14400 C is a huge number of charged particles, but the total loss of potential energy will just be their total charge multiplied by the voltage difference across which they move:

ΔPE_elec = q ΔV

= (14400 C)(12 V)

= 520 kJ