Question

Why AA batteries run exactly 1.5V?

Answer 1

 We all run into a situation when batteries in our remotes, toys, keyboards/mice run out. If we don't know how to check a battery we might throw out a perfectly fine battery (especially when we have a pile of them somewhere in the drawer).  

This electronics tip has to deal with checking common alkaline AA/AAA batteries or AA/AAA rechargeable batteries for proper voltage with a voltmeter.

Disclaimer : some people might say that a battery should always be tested under load but I have found that in most common household applications this is insignificant and will not change the results of the testing too much. 

Answer 2

They don't.

Just for you, I pulled seven (7) AA cells out of a fresh pack from the
store, taped them down to my desk, collected a few other things,
and made these measurements:


AA Cell     Open     at 25 mA     Calc int R, Ω   
     #1         1.596      1.546                  3.285
     #2         1.601      1.551                  3.285
     #3         1.598      1.539                  3.876
     #4         1.578      1.548                  1.971
     #5         1.600      1.539                  4.008
     #6         1.598      1.526                  4.730
     #7         1.600      1.547                  3.482

The (open/unloaded) voltage of the cell is determined by
the cell's "chemistry" ... the actual chemicals and metals
it's constructed from ... that undergo the chemical reaction
to deliver current between the terminals when a conductor
is connected there.

-- The variation in voltage among these 7 cells is about  1.44% .

-- The variation in the internal resistance of these cells ... an
indication of how much current (amps) a cell can deliver ...
varies over a range of almost 140% .  I am surprised.