What happens when we ground an AC circuit appliance and DC circuit appliance were grounded together when there is high voltage passing through the circuits?

 

If your household AC service is properly grounded there should be no problem. In the US, that implies a third conductor present at all outlets with a ground wire that does not conduct current.

If the DC supply is realized through a transformer that give galvanic isolation from the AC supply, the DC ground may be referenced to the AC ground with no current flow resulting.