|MadSci Network: Engineering|
There are a few reasons why household 1.5 Volt batteries are available in different sizes. Batteries convert chemical potential energy directly into electricity. For a given battery type, e.g. Alkaline, Zinc-Carbon, etc., the capacity of a battery is directly proportional to it's size. Additionally, the maximum current a battery can deliver is directly related to the area of the plates used. Car batteries can deliver as much as 500 Amperes for short periods because they have large plates with low internal resistance. A 12-Volt lantern battery can't get close to that high rating because their plate area is significantly smaller and their internal resistance is higher. A lantern battery might develop the right voltage, but it has no chance of starting your car. A typical "D" cell will last a lot longer than a "AA" or "C" cell for a given load because it simply stores more energy. The "D" cell is also capable of delivering much higher currents than their smaller counterparts. This is usually not necessary in consumer applications, but it's a direct result of larger plate area.
Battery manufacturers are constantly researching battery chemistries and materials in order to produce smaller, higher capacity batteries that are cheaper to manufacture. Cost, size, capacity, and weight are factors that must be compared when choosing a battery for a particular application.
The other reason batteries come in different sizes is simply a matter of practicality. A big battery will last a long time, but if it doesn't fit in your mini-maglite, it's no good.
The converse question is also interesting: why do so many batteries produce the same voltage? This is partly due to battery chemistry and partly due to customer demand. A "D" battery is technically not a battery, it is a single cell. Some of the first commercially available cells, e.g. Zinc-Carbon, produced a nominal 1.5 volts, this was due the materials used. Newer cells using different materials, like Manganese-Dioxide, would be required to develop the same voltage if they were used as replacements for Zinc-Carbons. Surprisingly, many of the materials used in modern cells produce voltages ranging from 1.1-1.7 volts. Higher voltage batteries, like 9-volt and 6-volt lantern batteries are made up of several cells in series. If you have a dead 9-volt battery laying around, you can see the individual cells by carefully peeling off the casing. Avoid breaking any of the individual cells, you might expose yourself to noxious chemicals. Alkaline 9-volt batteries are the most interesting, they are made up of 6 cells that are smaller than the standard "AAA" cell.
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