[MrFixr55]

+1 on Arran's and Morzh's comments. One should not get an AC Hum on a battery set. The ARBEIII is generally very well filtered. Is the hum there with the volume control all the way down?

The chassis and power transformer of an ARBEIII is grounded but I don't believe that the B- or any other terminal of the supply is grounded. You may need to check into that. Does the hum vary with tuning? If so, it is due to EMI interference. If 120 Hz hum, then there is an issue with the ARBE power supply.

Although I have an ARBE, I power the filaments of my 2V farm sets with a 3V PS and a resistor appropriate to drop 1V. The value of the resistor varies depending on tubes used. For example, for this set, the total current draw for all of these tubes in parallel is 0.5A. Per Ohm's law, to get a 1V drop across a resister where the total current draw is 0.5A, a 2 Ohm resistor is needed. Use a 2 W or higher. Belie e it or not, a 3V 1A Wall Wart switcher does not inject hum into the filament string, and in my experience, did not increase the (already high) EMI noise in my house.

Farm radios came in several different varieties depending on the region sold. Some areas had mechanization such as tractors and cars, some had generator-based power plants, either 6V or 32V, charging lead acid storage battery banks. Some had windmills charging batteries. Farm radios for these farms would run on 6VDC like a car radio or 32VDC. The 6V radios used vibrator power supplies for B voltage like car radios did. The 32V radios often used 32V as the plate voltage using specialized output tubes such as the '48. Sometimes on the 6V sets, schemes would be used to keep current draw to the minimum, such as using 2V battery tubes and a 4V to 135V vibrator supply (like my RCA 5BT and 6BT sets had an option for) or used 6V tubes that had lower current draw (like Zenith), or used 2V tubes in series parallel (like Silvertone), or merely used car radio tubes and circuits. Most of the sets using 2V tubes, A and B batteries used a C battery. Many of these sets used Class B audio output of about 2W using a '19 or 1J6 Dual Triode, compared to between 2 and 3W for a single end output transformer powered set. However, distortion was somewhat higher on these sets due to inherent "crossover" distortion on Class B output stages. However, Class B stages had lower "quiescent" current draw than Class A output stages.

Sets using 2V tubes were made from approximately 1930 to 1938 and fell by the wayside when sets based on the Sylvania 1.4V tubes (1A7 convertor, 1N5 RF or IF amp, 1H5 Diode-Triode detector, 1st AF Amp, 1A5 or 1C5 Output tube or 1Q5, 3Q5 Beam Power Output tube) were introduced in 1938-1939 along with the Loctal and Miniature variants of these tubes introduced in 1940. These sets ran on 1.5V A batteries, 90V B batteries. No C Batteries were used; bias was provided by a resistor in the B- line. Audio output was much less than the 2V sets; anywhere between 0.1W and 0.2WThe circuits for these 1.4V /90V battery "Farm" sets were virtually identical to the portable radios introduced at the same time.

Sets for farms that had no power available traditionally ran on a 2V lead acid battery and dry cell B Battery packs. Individual 2V lead acid batteries were available, or the user used a 6V car battery that may have had other uses in the house such as lighting and connected between the negative terminal and the first inter-cell strap. Back in the day, the connecting straps between cells of the battery were very accessible at the top of the battery. (Youngsters will not remember this, as internal straps came around only in the 1960s. Some industrial lead acid batteries still have these top of the cell straps.)

Of course, the lead acid battery needed to be charged. If there was no electricity from a windmill or generator, or mechanization available on the farm, the owner would have to carry the battery to a "service station" to have the battery charged. If this was too inconvenient, a 3V carbon-zinc dry cell A battery was used. A dropping resistor had to be used. In some sets, particularly Silvertone (Sears, Roebuck and Co, a BIG mail order supplier to farms), the resistor was a rheostat, because as the A battery aged, the voltage dropped.

Enter the Eveready A-600 Air Cell, a disposable battery that once "activated", provided a stable voltage, nominally 2.5V (but possibly really 2.35V) that remained the same until the battery was exhausted. A description of this as well as B and C Batteries is in this document by Eveready (National Carbon, part of Union Carbide), retrieved from the World Radio History website (a valuable resource for radio history information):

https://www.worldradiohistory.com/Archiv...1937-2.pdf

Hope this all helps.