You can't find these batteries at your local hardware store!

In the early days of electronics, vacuum tube devices were powered by batteries as many homes had not been wired for electricity. The batteries used for powering these early electronic vacuum tube devices were classified as "A", "B", and "C" batteries.

The "A" battery was used to provide power to the filament of a vacuum tubes in the device. Typically this battery was low voltage (usually between 2 to 7.5 volts) but required a high amperage to power the vacuum tube filaments. Lead-acid types, like classic car batteries, were used initially until better high amp-hour Zinc-Carbon batteries were developed.

The "B" battery was used to provide the plate voltage of a vacuum tube. These were typically of Zinc-Carbon variety with many cells wired in series to provide the low amperage and high voltage (usually 22.5, 45 or 90 Volts) required.

The "C" battery was used to provide bias to the control grid of a vacuum tubes. This was typically a low voltage and low amperage (9 Volts  with several 1.5 Volt taps) Zinc-Carbon battery. The C battery was largely done away with as it was soon discovered that the needed voltage/current bias could be derived from the "A" battery using a grid leak resistor or voltage divider biasing.  

Pictured about are examples of an "A" and "B" battery I just pulled out of a 1947 TRAV-LER Model 5020 portable vacuum tube radio that I am in the process of restoring. Two "A" batteries were connected in series to provide the required 9 Volts for the tube filaments. In addition, two "B" batteries are connected in series to provide the required 90 Volt plate voltage. No "C" battery is required as the Model 5020 uses grid leak resistors to provide required voltage.

I plan on gutting these vintage "A" and  "B" batteries, then installing modern batteries wired in the proper fashion to achieve the proper voltage/current required.