What is the German word for 'blown' when referring to something that has burned out?

The German word for 'blown' when referring to something that has burned out is indeed 'durchgebrannt'. This term is commonly used to describe a fuse or bulb that has failed due to excessive electrical current, resulting in a burn-out condition.

The structure of the word 'durchgebrannt' comes from the combination of 'durch', meaning 'through' or 'by', and 'gebrannt', the past participle of 'brennen', which means 'to burn'. This indicates that something has burned through or has effectively burned out.

The other options do not fit the context of something being 'blown' in terms of burning out. 'Anzeige' translates to 'display' or 'indicator', which doesn't relate to the concept of failure due to burning out. 'Kartusche' refers to a cartridge, often used in the context of ammunition or ink, and likewise has no connection to burning or electrical failure. 'Buchse' means 'socket' and does not imply anything about burning out or failure due to excessive current. Thus, 'durchgebrannt' is the only choice that accurately conveys the meaning of something that has burned out.