Questions about power transformer. (Step Down, 220 --> 110)

It seems that all of the larger (bigger than 300W) power transformers I have will noticeably hum when plugged in to the wall, even when there is nothing plugged into the unit. What causes the humming? Is there actually current flowing and/or power being consumed. I know that “current” and “power” have specific definitions in electricity discussions, and I might not be using them correctly. Basically, I’m wondering if a plugged in power transformer is costing me money at the meter, even when it is not in use. I have some 300W units that are nice and quit. Are these things costing me money, even when the television plugged into them are off? What about the larger, noisier ones?

Yes, they are costing you money. Maybe not much, but measurable.
Feel the transformer- is it warm? That’s where your money is going.
An unloaded transformer is wasting energy by heating the imperfect core.

Measurable like the flashing clock on the microwave? Or more like an LED nightlight? Or something else?

Larger such converters will have a transformer. Transformer hum is sometimes quite noticeable.

No-load transformer noise is typically due to magnetostriction causing parts like the transformer core physically to get larger and smaller each cycle. Other magnetic effects also result in core vibration.

You can buy quieter transformers for both loaded and no-load conditions but they typically cost significantly more.

Thanks.

Also something strange: In one room, there are two outlets on opposing walls. Both outlets are connected to the same breaker. With nothing plugged in to it, connecting the 1000watt transformer to one of the outlets will trip the breaker, but inserting it into the other outlet does not trip the breaker.
Why would a transformer with no load trip the breaker, and why would that reason not cause the breaker to trip using the other outlet?

my guess is that the first outlet is “downstream” of the other one, and has an internal fault which causes a short (thus the breaker trip) when you plug something in.

My guess:

The breaker is tripping due to the magnetization inrush current. This can be substantial, depending on the state of the core magnetization from the last time the transformer was disconnected. Either the additional resistance of the wire to the far outlet is enough to keep the breaker from tripping, or you have just gotten lucky.