I'm designing the simple project of "Ding Dong bell". This circuit should be very small and cheap and will be place in a small plastic cavity. To convert AC/DC voltage I can't place any transfor mer in this circiut due to it's large size. If I devide voltage by a big resistor or chop it, is it safe? Does it get too much hot to burn or fire?
You shouldn't be playing with dangerous high voltage mains wiring if you don't know how to simply calculate the power in a resistor.
Use a transformer so you don't electrocute anybody.
You can of course mount your transformer remotely from the bell as is often done in practice. The power resistor you need might cost more than the rest of the project.