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In the datasheet for fuses (for example, I'm looking at the Bel Fuse 0678L9150-02 -- datasheet at https://www.belfuse.com/resources/CircuitProtection/datasheets/0678L%20Jun%202016.pdf), they report the melting I²T integral (in A²·sec), but they say @ 10 In --- not sure whether the first letter is a capital-i, or lowercase-L.

  1. What does In (whatever the right spelling may be) mean in this context?
  2. What does the Time-Current characteristic curve tell me? For example, in the above fuse model, if I look at the 10A curve (presumably that means the curve for the fuse with 10A rating), then 20A maps to 5 sec. Does that mean that if a fixed current of 20A runs through it, after 5 sec it will blow? (understanding that this is a "theoretical" / average figure). What doesn't seem right about this is that the curves get to very high amounts of time --- I mean, it doesn't make sense that the stress would be cumulative at such a slow rate until reaching an amount of accumulated stress that makes it blow.

I guess this brings me to a more fundamental doubt I have: what does the Amp rating really relate to? Is it:

  • the point at which the fuse should blow? (meaning that normal operating current should be, say, half or a tenth of that value?)
  • the maximum normal operating current? (meaning that the fuse will blow when the current exceeds that value by a factor of, I dunno, 5 or 10 times that?).

I suspect that strictly speaking it is neither, and that one has to do somewhat more involved calculations?

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What does In (whatever the right spelling may be) mean in this context?

It is \$I_n\$ and it indicates that the measurements were taken at 10x the nominal current. The best example might be the 30 A fuse. A rating of \$1000 A^2 s\$ means that at 300 A it should blow around 0.011 s. That lines up roughly with the graph.

What does the Time-Current characteristic curve tell me? If I look at the 10A curve [...] then 20A maps to 5 sec. Does that mean that if a fixed current of 20A runs through it, after 5 sec it will blow?

Yes.

What does the Amp rating really relate to?

The amp rating on the face of the fuse is the nominal current. A 10 A fuse can operate indefinitely at 10 A. However, as you've seen, this 10 A fuse can also operate at a steady 15 A for ~1.4 hours. All fuses are designed to open during a short circuit but the time-current characteristic will give you an idea of the rest of its operation.

Try looking at the time-current characteristics of "fast-blow" and "slow-blow" fuses. You'll find fuses that can operate at 1 A indefinitely, but will blow at 2 A within 0.1 s. It all depends on your application.

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