Breakers only control hot-wires, not neutral-wires nor ground-wires FYI.
So it doesn't matter if the appliance is on the same breaker or a different one, the hum can still exist in both cases.
All neutral and ground wires are shared with ALL
the appliances in a house, as one large circuit; independent of the breaker it uses.
and THAT enables the problem to exist.
What further enables the problem, is that RCA cables and the HDMI wires allow power to flow through the ground wire between devices.
Optical cables are immune to this effect; not sure about XLR cables, they are probably noise-resistant at least.
If all cables were shielded on both ends to a common ground, and the signal-grounds were floated but shielded from noise, then ground hums would be rare. But that ideal is never achieved.TV box cables are known for inducing grounding issues 99 out of 100 times
; this is because they are grounded at a different point to the earth, increasing the chance of a voltage difference.
Most hums are induced by induction from things such as fan motors and transformers, or a malfunctioning device that are bleeding line power.
I had a similar issue last week.
Turns out it was the HDMI cable between my TV cable box and my sound processor, it induced a hum in my RCA cables to my BFD, and all down stream amps.
The cable box itself had no ground plug (not grounded), but my sound processor IS grounded, so the power from the cable shield decided to use the grounded HDMI wire as a return path, which is the same ground that my RCA cables use.
The cable box grounded their HDMI port to the floating Cable shield instead of earth ground (made in China, that's all I have to say
All it takes is a few miliohms or milivolts upon the shared ground, and presto, a hum is born.
My temporary solution was to unplug the HDMI cable.
I'll have to look into grounding their coax cable as a more permanent solution.
Mark is correct BTW, you have to disconnect all conductor paths, turning a device off is almost never sufficient.