BTW what does amp hours mean exactly ?
An ampere hour (abbreviated Ah, or sometimes amp hour) is the amount of energy charge in a battery that will allow one ampere of current to flow for one hour.
Technically speaking, an amp-hour (Ah) is a unit of charge, but in practical usage, it is a unit used to describe the storage capacity of a battery.
First, here is a technical explanation of the amp-hour unit. The unit is created by multiplying amps (a unit of current) by hours (a unit of time, obviously). Amps are a measure of the rate of flow of charges, and so we can break the amp unit down into coulomb’s per second. Since an hour is 3600 seconds:
the unit of Amp-hours = coulombs/second times 3600 seconds = 3600 coulombs
What does this mean for a battery? Well, in theory, it means a 1 Amp-hour battery could provide 1 amp of current for an hour (3600 coulombs of charge), or it could provide 0.5 amps of current for two hours (still 3600 coulombs of charge), or 6 amps of current for 10 minutes (still 3600 coulombs of charge). Also, in theory, if you know the voltage of the battery, you could determine the amount of energy that is in all of those charges. Since a volt is a joule/coulomb, and with an Ah measurement, you know how many coulombs of charge you have, you could figure out the amount of energy stored in a battery. For example if you have a 12 volt, 18Ah battery, the amount of energy stored in it is:
12 joules/coulomb * 18 coulombs/sec * 3600 sec = 777,600 joules
Of course, this is only true if we make several assumptions (none of which are true)
The battery voltage doesn’t change as the charge in the battery is depleted
The battery voltage doesn’t change if the load changes
All of the energy in the battery can be put to use
All of the coulombs are available no matter what kind of load you put on the battery.
In reality, the bigger the load, the lower the amp-hour rating will actually be and also as your battery is drained, the voltage output by the battery also drops. So the amp-hour rating is really just a guide to approximately how long it will last.