I've been looking over the table in GN3 for the resistance of copper conductors per meter and there is something causing a form of OCD to manifest in me 'ead.
It's obvious that if you double the length of a conductor it will double in resistance and if you halve it, it will halve in resistance. It should also follow that if you double the csa, it would be the same as halving the length and vice versa.
Now, here's the bit that's tickling at my OCD, or my maths is wrong somewhere.
We have to start somewhere, so I'll take the 1mm2 conductor resistance @20 deg as read at 18.1 m ohms per meter as the constant.
Surely I should be able to work out the 2.5mm2 resistance per meter from that with the following...
First get the multiplier from the ratio...
1/2.5 = 0.4
Multiply the constant from 1mm2 by that ratio...
18.1 x 0.4 = 7.24
But the table says that for 2.5mm2 it's 7.41.
As another example and just for the hell of it, we'll pick a much larger conductor of 25mm2
1/25 = 0.04
18.1 x 0.04 = 0.724
Again, the table doesn't agree giving 0.727
This method comes close in all cases, but is never on the money. Is my maths flawed here? It could be the original constant of the 18.1 for the 1mm2 conductor that I chose. Does anybody have a mathematical formula to link these resistance per meter values? It would be nice to work these out rather than trying to remember them. I can of course just do as I do now and just refer to the values in the table, but this is just a mental exercise to stop the ol' brain cells dying off.
It seems to me that the absolute of double the length, double the resistance and halve the length halve the resistance doesn't work so well for the csa of the conductor when looking at the table.
It's obvious that if you double the length of a conductor it will double in resistance and if you halve it, it will halve in resistance. It should also follow that if you double the csa, it would be the same as halving the length and vice versa.
Now, here's the bit that's tickling at my OCD, or my maths is wrong somewhere.
We have to start somewhere, so I'll take the 1mm2 conductor resistance @20 deg as read at 18.1 m ohms per meter as the constant.
Surely I should be able to work out the 2.5mm2 resistance per meter from that with the following...
First get the multiplier from the ratio...
1/2.5 = 0.4
Multiply the constant from 1mm2 by that ratio...
18.1 x 0.4 = 7.24
But the table says that for 2.5mm2 it's 7.41.
As another example and just for the hell of it, we'll pick a much larger conductor of 25mm2
1/25 = 0.04
18.1 x 0.04 = 0.724
Again, the table doesn't agree giving 0.727
This method comes close in all cases, but is never on the money. Is my maths flawed here? It could be the original constant of the 18.1 for the 1mm2 conductor that I chose. Does anybody have a mathematical formula to link these resistance per meter values? It would be nice to work these out rather than trying to remember them. I can of course just do as I do now and just refer to the values in the table, but this is just a mental exercise to stop the ol' brain cells dying off.
It seems to me that the absolute of double the length, double the resistance and halve the length halve the resistance doesn't work so well for the csa of the conductor when looking at the table.
