I'm not sure how hot the actual filament will be surrounded by insulation and water presumably at 100°C.Tell me how hot the heating elements will be 'after the initial few minutes' and I'll do the approximate sums for you
They are according to the measurements, e.g. immersions are 3kW and around 19Ω when cold.
Lamps are different
You're obviously thinking of elements immersed in water (kettles, immersions etc.) and, as we've often discussed, goodness knows what temp the actual element runs at - obviously at least 100°, probably a lot higher. In the absence of cooling by water, elements coud get much hotter. For example, fan heater and hair dryer elements start glowing red hot (several hundred degrees) almost immediately if the fan slows or stops, so I suspect usually runs very hot. Similarly, toasters run red hot all the time.I'm not sure how hot the actual filament will be surrounded by insulation and water presumably at 100°C. It could be much more than 100°C.Tell me how hot the heating elements will be 'after the initial few minutes' and I'll do the approximate sums for you
Fair enough, even if a bit tangential to this thread (one doesn't usually plug immersions into BS1363 sockets!). If that's the case then, as you're implying, 19Ω equates to 3.03kW (12.63A) at 240V (seemingly to voltage at which most ratings are quoted) - so 3kW (at 240V) does, indeed, appear to be the cold rating. If we assume that's at 20°C, and that the absolute minimum 'running' temp is 100°C, the resistance would then have risen to abt least 25Ω - about 2.3kW (9.6A) at 240V.
I was just using that as an example.
They must be (worst case) otherwise design considerations would be inadequate.
Thank you.
Fair enough - the pattern certainly seems consistent.
On the basis of the cold resistance figures you're quoting, it does seem to be the cold rating - but I don't think your 'must be' necessarily works. If it's only for the first few seconds, or even a minute or two, we are happy to design (cable CCC-wise) without taking the initial current of, say, a filament lamp or motor into account.
That statement needs a fair bit of qualification
IF the loads are both 3kW resistive at 240V when element temperature is 20° and IF the normal running temp of the element is at least 100°C, then the total load when running (on 240V) would be less than 20A. 
Why would it be?
You appear to be assuming that the elements are made of copper.
In that case, it obviously wouldn't be. As in the other thread to which EFLI referred, in the absence of knowing what metal(s) we are dealing with, I used a figure of 0.004 which is the rough ballpark of coefficients for many metals (including copper, aluminium, lead, gold, silver, platinum, tungsten, even iron). If you know that the heating elements we're talking about use nichrome, then your calculation would obviously be appropriate.
... or, as I've just written, aluminium, lead, gold, silver, platinum, tungsten, or iron etc. etc. - in fact probably most 'common metals' other than nichrome (if you call nichrome common!).
Yes, come to think about it, I believe you're right - either that or various other alloys, the coefficients of resistivity of which i wouldn't know!
I certainly doubt copper, but wouldn't be too surprised by tungsten.
Of course not - I was merely illustrating that the coefficient is in the ballpark of 0.004 for 'many (elemental) metals'.
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