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kA^2s

Nathaniel
This is not something I need answered: I already have a view - although someone might manage to change it. It's hoped to be a quiz-like stimulus to think about caution with units and prefixes. A comment here a week or two ago prompted me to look again in a standard - this time IEC61008-1 (2010). There I noticed a table of peak currents Ip and 'let through' I2t, that the devices are tested with. Here's a small excerpt,

81e202a88c2cf17c4a84e9cec5efcc52-huge-ka2s.png


The columns give test values for RCDs that have rated currents 16 A and 20 A and with rated withstand of 6 kA 'prospective'. (The low Ip values are reasonable if the RCD is expected to be protected by a current-limiting device rated close to its own rated current In.) 


It seems that the unit they give for I2t is used in a way I've also seen in one manufacturer's specifications for MCBs/fuses.
But is this 'correct'?  

A comparison to mm^2 might be helpful. 



The login process reminded me of another question that often occurs when seeing the IEE building, or logging into a 'thexxx.org' website: nearly 20 years on, is there anyone who sees a benefit of the change from IEE to THEIET? Too late now, in any case. One can hope the name doesn't make too much difference to what happens either way, although I feels the lack of mention of electricity is a bit strange for the institution's current or past work. I wonder if the cynical view I had at the time of the vote was actually unjust. 

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    J/Ω looks a very good idea, as it avoids any exponent. Then kJ/Ω works without confusion.



    Yes, k A2s with the definite space strikes me as clear (103 A2s). However, this is not what is written in the IEC table that I showed - that has no space. And it appears that a space here would not be permitted by the SI rules, as prefixes are "attached to unit symbols without a space between the prefix symbol and the unit symbol". Note also the point about milli and metre having the same letter, which could lead to confusion in some cases if prefixes were left standing about by themselves. So, for an organization that strives to follow SI, I think replacing k with 103 would be the safest option to avoid ambiguity. If it's happy to bend the rules a bit in this case, like others Graham mentioned, then the space is probably clear enough, and parentheses even safer.



    (On eV: the reason there's an e in the symbol is as you mention. But if we use the symbol in the way the SI system tells us [Table 8] it's a single symbol, regardless of its history. If we wanted to write an electronic charge multiplied by a volt, the former would be a quantity symbol rather than a unit, so would conventionally be italic.)



    I suspect our difference here arises because you're considering what would be clear to a technical user, and I'm considering from the view of what happens if SI rules are strictly applied. If we go back to the original question, note that there was no space after the k in the table, which leaves us with the kA2 versus mm2 point that Andy has summarised well.


    [Edit! Now I've seen the update [mapj1] and further point [ebee], after posting. As long as the Americans keep dollar signs before numbers I suppose we're safe with our habits in that way.]


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    Surely, the problem is in the SI Specification itself not being correct in mathematical notation.


    For example, "square kilometre" is (km)2 or k2m2 and this makes full mathematical sense of how the standard multiplier is addressed in numerical terms.


    Defining "square kilometre" as km2 unfortunately makes no mathematical sense, and has led to examiners being able to set "trick" questions in physics and maths exams!
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    gkenyon:

    Surely, the problem is in the SI Specification itself not being correct in mathematical notation.


    For example, "square kilometre" is (km)2 or k2m2 and this makes full mathematical sense of how the standard multiplier is addressed in numerical terms.


    Defining "square kilometre" as km2 unfortunately makes no mathematical sense, and has led to examiners being able to set "trick" questions in physics and maths exams!


    What's wrong with having a square Amp?


    We can all imagine a field of 1 square kilometre being ruled out into a million metre squares, but I cannot quite visualize an Amp let alone a square Amp. The fact remains that under the SI system, the unit kA2s is a square kiloamp second so I agree with Nathaniel.


    However, I cannot find any explicit reference to SI units in IEC 61008-1:2010, so perhaps they can do their own thing after all.

     


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    Chris Pearson:
    gkenyon:

    Surely, the problem is in the SI Specification itself not being correct in mathematical notation.


    For example, "square kilometre" is (km)2 or k2m2 and this makes full mathematical sense of how the standard multiplier is addressed in numerical terms.


    Defining "square kilometre" as km2 unfortunately makes no mathematical sense, and has led to examiners being able to set "trick" questions in physics and maths exams!


    What's wrong with having a square Amp?


    We can all imagine a field of 1 square kilometre being ruled out into a million metre squares, but I cannot quite visualize an Amp let alone a square Amp.




    Nothing wrong with A2s at all

     



    The fact remains that under the SI system, the unit kA2s is a square kiloamp second so I agree with Nathaniel. However, I cannot find any explicit reference to SI units in IEC 61008-1:2010, so perhaps they can do their own thing after all.

    Well, this depends on how you interpret the SI system ... is the unit being discussed an A or an A2s. If the derived unit is an A2s, then kA2s is a possibility for 1000s of A2s, but an alternative interpretation is that kA2s is equivalent to 1,000,000 A2s.


    All of which would have been solved if the SI Specification was mathematically correct - which it is definitely NOT.
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    On the SI specification's mathematical correctness.

    This depends on how one views a prefix&unit combination. They may look like a product, particularly when each of the pair has a single-letter symbol (like mA, but not kPa for instance). If they are a product, the claimed meaning of mm2 etc would indeed not fit with widely used rules of precedence of products and exponents. 

    But what the specification says (as quoted earlier) is that the prefix and unit together form a "new inseperable unit symbol": it is not treated as a product of a numeric multiplier and plain (coherent) unit, but as a single symbol.  So there's no product that needs mathematical rules applied when it's raised to some power: there's just the single symbol such as a kV, mm, MPa etc.  

    In this way, there's no mathematical incorrectness about how mm, kA etc behave when put to positive or negative powers. 

    Is the unit being discussed an A or A2s. If the derived unit is an A2s, ...

    A2s is indeed a derived unit. But does the SI permit prefixing of a compound derived unit? That is, one that includes multiplication, division or exponentiation of unit symbols, not  just a single symbol.  I see nothing saying it does. Consider "Prefixes may be used with any of the 29 SI units with special names with the exception of the base unit kilogram": this permits prefixing the single-symbol units, which are the base units and the 22 specially named derived units. As noted before, it doesn't explicitly forbid prefixing compound units, but doing this would clearly create a trouble if prefixes must be without separator and form a new inseparable symbol, etc, while the parts within a compound unit should be separated from each other. The strongest argument I see, anyway, for whether to prefix compound units, is that there's nothing to say it can be done (or have I missed it?). 


    As long as we stick to what's actually said, rather than how we've been used to thinking of it (perhaps from much older practices such as combined prefixes, or everyday practices of writing 10k for 10 000) it appears to me to be an unambiguous system.  Thank you for helping me to dig further into this document's not-crystal-clear depths! I hadn't gone in to some of those details before. 


    I'll let you know if the IEC gives a verdict - I wrote a quick note last week, just thinking it wouldn't hurt them to correct it for the next time, even if it's never really going to matter.  I'd be amused if they claim they've got their own system.  But I really doubt they'd formally claim that. 

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