Almost all of the batteries at the store, A, AA, AAA, C, D, they all have the same voltage. To get a higher voltage you have to chain them positive end to negative end. That’s why batteries are normally placed in alternating directions in a device.
So 3 AAA batteries gets more voltage, and that is important for some applications.
Most likely this is the case: The device needs a voltage, say 4.5V. Batteries are about 1.5V, so you need three batteries. Using 1 or 2 won’t work, voltage too low. Whether it’s AAA or AA depends on how much power the device needs to draw, usually balanced with the room the device has for batteries.
The amount of batteries you use sets the voltage – each AA or AAA cell produces 1.5v, and this voltage adds up, so if your device runs on 4.5v, you can chain together three 1.5v cells to make 4.5v.
The size of the batteries sets the battery life – an AA and AAA battery are essentially the exact same thing, only an AA is a little larger – this allows it to contain more chemistry, so it produces a bit more power.
So the quick rule is that a designer will choose the amount of batteries based on the voltage needed, and the size is a balance between battery life and physical size.
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