Some physics books said that the fuse rating is the maximum current that the fuse can carry without melting it. But some said that the fuse rating is indicating the current at which the fuse would immediately melt. Which is true?
Answers and Replies
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Fuses are rated according to the current which they will pass without melting. A full specification for a fuse will show curves giving the length of time a specific current will cause a typical fuse (of the given specification) to blow. As an example, see page four of: http://www.bussmann.com/library/bifs/5022.PDF
Note that in the above diagram, the curve for the 3A rated fuse shows that it didn't blow below 4 amps. In other words, that fuse is supposed to carry 3 amps forever.
In actual use, I've seen fuses that apparently blew at their rated amperage, but that's not what the specs show. Maybe the circuit really takes more current than I thought. Maybe the fuse was defective. But the spec is clear. The fuse passes the rated current without blowing.
The difference between slow blow and fast blow fuses is in the shape of those curves, not the current that blows them in the steady state. In other words, if you draw a fast blow and slow blow curve on the same graph, the fast blow curve will be sharper, but they will intersect the long end of the time scale (i.e. the top of the graph on page 4 of the above link) at the same amperage (i.e. about 4 amps for a 3 amp fuse).
As far as transients go, all fuses will fail to blow if a transient of a given magnitude is sufficiently short in time. A fast blow fuse will blow on shorter transients than slow blow fuses. This is another way of saying that the "blow" side of their graph includes more territory in the above graph, but no fuse has a graph with a square corner (at the bottom left corner of the above graph).