So, its normal for the radio to stay on even if the adapter is removed
from the wall outlet with the cable still plugged into the power jack?

Thanks

Is it normal when using the radio with an AC adapter, that if you unplug
the adapter from the wall outlet with the cable still attached to the
radio that the radio still operates?

I thought that when connecting the power cable to the radio that the
internal batteries are disconnected by the power jack.

Thanks

Electronic switching.