Electronic – replace a 12a fuse with a 15a fuse on a 12v – 120v automobile inverter

a. grounded negative chassis is a convention, it can be a grounded positive instead, but every connection has to be reversed. ground is a concept, a point of reference, but not a physics reality.

b. the current passes through the battery positive terminal and the fuse, and so it doesn't matter what the return path is; a negative cable or chassis. the fuse will still blow on fault. the fuse has to be part of the circuit for it to blow.

c. there is no alternative route, the current must pass through the fuse. it may also pass through other things, but this is not important; the fuse will still operate if the current and time allow it to.

d. the alternator has a cable connected to the battery positive, and either a cable connected to battery negative or the chassis is used as the path. it works because the alternator generates a voltage higher than the battery, and the voltage carries power into the battery. during charge, the battery is a load with respect to the alternator.

There are more things to consider.

First: Note that the vacuum taking only 1100W, i.e., 5A, could still draw a very short peak of much more current when the motor starts; it really depends on how exactly are these 1100W calculated.

Second thing: Is the 13A fuse in the cleaner accessible? Could you exchange it for a 10A fuse? The only thing that can happen then is that the fuse blows up unexpectedly.

Third thing: Is spending couple bucks for a 15A rated switch that much a problem?

While I don't think your house will catch fire because of this (since 1. mostly when something goes wrong, the current drawn is much higher than what it should be and should blow up your 13A fuse and/or your circuit breaker long time before the switch heats up to ignite and 2. the 10A rating of the switch means it should withstand much more in practice, there's a certain safety margin), I wouldn't recommend violating the rules of the game, since in this game, the game over could be quite serious.