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I am trying to verify that I have correctly understood how to size a fuse to protect circuit components.

Lets assume I have a resistor model series that can tolerate 60W for 1 ms according to the datasheet (0.33W continuous). Let's also assume the resistor chosen has 1k.

For the sake of argument lets assume this resistor is connected between a voltage source and ground and shall be protected against damage by over-voltage with a fuse.

My approach would be to calculate a maximum permissible I²t rating of the fuse as follows:

R*I²t <= P*t
I²t <= P*t/R
I²t <= 60W * 1ms / 1k
I²t <= 6e-5 A²s

So any fuse with I²t < 6e-5 A²s should protect the resistor (minus some margin), right? Of course the fuse must also tolerate the nominal current indefinitely...

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  • \$\begingroup\$ Why wouldn't you choose a resistor that can handle the overload conditions that may present themselves and forget about using a fuse? \$\endgroup\$
    – Andy aka
    Commented Feb 12, 2023 at 19:40
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    \$\begingroup\$ Normally you're not trying to protect one component -- rather, you're trying to protect a module within a system from the system misbehaving, or you're trying to protect the system from a module that's misbehaving. So you might have a fuse on the power entry to the board, but that's for some combination of protecting the wiring to that board, and (sometimes) trying to make sure that a 1-point fault on the board will blow the fuse and leave the board in a repairable state. \$\endgroup\$
    – TimWescott
    Commented Feb 12, 2023 at 19:44
  • \$\begingroup\$ Is your note "(0.33 W continuous)" intended as supplementary information, or do you mean that you somehow calculated the 60 W for 1 ms number from that? Because in the latter case, something's gone wrong, because you can't just calculate that like that--I've seen enough people get it wrong on here that the particular way you wrote that out has me wondering, is all. \$\endgroup\$
    – Hearth
    Commented Feb 12, 2023 at 19:57
  • \$\begingroup\$ @Hearth Yes, that was supplementary information. Thanks for the hint! \$\endgroup\$
    – ARF
    Commented Feb 12, 2023 at 20:13
  • \$\begingroup\$ @Andyaka This was merely a thought experiment. I was trying to check that I had understood how to calculate a required I²t rating. I probably should have been clearer. \$\endgroup\$
    – ARF
    Commented Feb 12, 2023 at 20:15

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Yes, assuming the fuse also acts with the rated I2t in the given time (1ms) -- in general it varies with time/current, as shown in the time curves. (The I2t measure is less dependent on time, or other device properties, than a pure energy, voltage or charge measure would be, but it does still depend.)

Note that the "minus some margin" will be pretty generous, as fuses are quite crude devices. Strictly speaking, matching the fuse's max. I2t to the component's min. is sufficient; in which case, this is just to say, expect a wider margin in the typical case.

For the given example, I would not suggest protecting a small (chip or axial) resistor with a fuse; rather, use a resistor rated for it in the first place ("fusible").

Power resistors (wirewound or composition, and film types as well when large enough) are generally big enough to protect with a fuse. Remember, fundamentally: the fuse protects the wiring. If the resistor is itself basically nothing but bulk wiring (like these types), it can be robust enough to be fuse protected. Always check the datasheet for pulse or fusing ratings and design accordingly.

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