A battery (vacuum tubes)

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Eveready #742 1½ volts
Portable "A" battery for 1.4 volt receivers
L 2.5" W 2.5" H 4" ca. 1942

The "A" battery circuit of a triode (white area)

In electronics, an A battery is any battery used to provide power to the filament of a vacuum tube. It is sometimes colloquially referred to as a "wet battery" (although there's no reason why a "dry" battery of suitable voltage couldn't be utilised for the purpose; the A battery in the photo is a dry battery.) The term comes from the days of valve (tube) radios when it was common practice to use a dry battery for the plate (Anode) voltage and a rechargeable lead/acid "wet" battery for the filament voltage.

The alphabetic designation of these batteries is derived from the historic identification of the elements of the vacuum tube. Initially, the only such device was a diode with only a plate and cathode. Following the direction of electron flow, these electrodes were identified as "A" and "B" for the cathode and anode (plate), respectively. Later, when the control grid element was added to create the triode tube, it was logically assigned the letter "C." Subsequent addition of the "screen grid" and "suppressor grid" to improve the performance of the triode, resulting in the tetrode and pentode, respectively, did not require an extension to this series of batteries. These grids were either resistively-biased from the existing batteries, or were connected to ground or the cathode.

The prior existence of the "A" battery is apparently the reason why there is no single-A battery (cell) size. In devising the lettered sizes for single-cell "batteries," it seems that there was a conscious effort to avoid single-A, while the omission of "B" was likely due to its association with a much higher voltage.