I have been reading literature on fuses and came across the joule integral or $i^2t$ value many times. Often, it is referred to as energy but I am confused because shouldn't energy be $E=RI^2t$? I would appreciate if you could explain what the joule integral is and its physical meaning.
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1$\begingroup$ If i^2*t is called energy , it is wrong, probably it is meant as proportional to it, since your fuse has a fixed resistance. So you should cite where you found this. $\endgroup$– trulaCommented Oct 24, 2020 at 19:42
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The Joule integral is actually used to characterize fuses. There are two extremes for specifying the current-carrying capability of a conductor.
a) Over a long time, all heat is lost to the environment. The current is given for some permitted temperature rise. Typically this is the temperature rating of the insulation.
b) Over a very short time, no heat is lost to the environment. This is the so-called adiabatic case.
As the power generated in a conductor is $I^2R$, the heat energy deposited is $I^2Rt$. For any given conductor, R is constant, so the energy (per unit resistance) to reach some temperature for the short-time case is usually given as $I^2t$.
For a fuse, typical temperatures are the 'guaranteed to still work' temperature and the 'guaranteed to break' temperature or melting temperature.
When you're protecting something else that has a quoted survival of $I^2t$, for instance a rectifier diode, you would want the rating of the diode to exceed the 'guaranteed to break' rating of the fuse, also known as the 'let-through' energy.
That's the reason we define $I^2t$ to express the amount of energy (per resistance) required to actuate the fuse.
answered Oct 25, 2020 at 5:17
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$\begingroup$ so removing the R is a convenient approximation, that also provides a margin of safety? $\endgroup$ Commented Oct 25, 2020 at 12:08
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