Your hunch that batteries have a current limitation is correct. In general, it's hard to tell the current rating [A] from capacity [A·h]. You have to look it up in the datasheet. A lot depends on the design of the battery.
For example: coin cells with 500mAh capacity may have only 3mA max current.
Another (opposite) example: automotive starter battery with 40Ah capacity may have 500A max current.
Lead-acid batteries are interesting in this respect, because there are two distinct types.
- Starter lead-acid batteries are designed specifically to deliver high peak current for a short period of time. Deep discharge, however, dramatically shortens the life of a starter battery. So, it's not suited for routine operation at high depths of discharge. Your typical starter battery in the automobile works at very shallow depth of discharge.
- Deep cycle lead-acid batteries are designed (as name suggests) to discharge further. But they can not provide as much instantaneous current.
Here's an example datasheet for a deep cycle battery. Have a look at the nominal capacity on p.1. Notice that capacity depends on discharge current (i.e. the rate of discharge).
-
Depth of Discharge Starter Battery Deep-cycle Battery
100% 12–15 cycles 150–200 cycles
50% 100–120 cycles 400–500 cycles
30% 130–150 cycles 1,000 and more cycles
(Source.)
p.s. If you want to read-up, here's an excellent web site on batteries - Battery University.
The amp hour rating means the battery can supposedly deliver 50 amps for one hour. Note that this could be 25 A for 2 hours, 5 amps for 10 hours, etc. In other words, it is in units of charge.
The voltage rating says it can do this at 24 V. Charge times voltage is energy, which is the energy the battery can supposedly deliver before being depleted. This energy is (50 A)(3600 s)(24 V) = 4.32 MJ.
Now look at what rate you are draining energy, which is (5 V)(100 mA) = 500 mW = 500 mJ/s. To drain the whole battery energy therefore would take (4.32 MJ)/(500 mW) = 8.64 Ms = 2.4 kHours = 100 days.
However, that doesn't take real world battery issues into account, and ignores inefficiencies in converting from the battery voltage to 5 V. Let's say the conversion is 80% efficient. Guessing what the battery can really do is more tricky. You have to look at the battery datasheet carefully to decide what its capacity really is under your conditions of discharge rate, temperature, age, number of cycles, etc. For a single use battery, you can be more aggressive. For a rechargeable, you need to derate more since the capacity goes down over time, with the number of cycles, how deeply it was discharged, how long it was held in various states.
Let's say that you've decided that due to the very low discharge rate for this battery, the temperature, etc, you will only get 30 Ah capacity at the end of its service life. That's 60% of the theoretical.
So in this example we get 80% due to power conversion and 60% due to battery usage, for a total of 48% overall. Therefore the estimate would 48% of the theoretical 100 days, so 48 days or "one and a half months".
Best Answer
From your own link:
Thus, the answer to your question:
You do this by multiplying by 0.7.