Let me begin with this, I use an in-home sound system to power my subs and use an inverter to power the sound system. The inverter is normally powered from the car charger outlet, but there wasn't enough connection being made so the inverter would cut out when the current increased.(When the bass hit hard)

So I wired the inverter to the cigarette lighter wires. I put a switch on the line so it doesn't drain the battery, obviously. When I first tested it I blew the fuse and added another fuse on the line next to the switch. Everything worked until later that day the bass hit REALLY hard and I blew the in-line fuse next to the switch. I looked at the fuse and noticed it said F3AL250V. I'm assuming that means it is a 3 amp fuse.

What confuses me how did the fuse not blow earlier since it was on a 20 amp circuit from the trucks fuse box in the first place? Will it hurt to put a 20 amp in-line fuse in place of the 3 amp??