AC

I was fooling around with the lights in the bedroom, which looks like it is on the DC circuit, i blew a 15 amp fuse. But at the time the AC was on, and i lost power to that when thefuse blew. The breaker for the AC was not tripped. So I wired off the lights so they wern’t in the circuit, and replced the fuse, and the AC came back on.
I don’t understand, I thought the AC was protected by the breaker labeled AC, not the blade fuse (15amp) labelled bedroom