Where can I buy 3mm green and yellow earth cable?

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Yet today we limit fixed appliances to 2kW without special calculations.

That is just not true and is not in the regs. What is more such appliances, washing machines, dish washers, tumble dryers, even some ovens over 2KW come with moulded 13A plugs.
OK I did not say with a ring final and I should have said with a ring final there is clearly no problem using a 13A plug and socket with fixed appliance when plugging into a dedicated radial or any other supply if we calculate the loads it is likely to encounter. To take two 2.5mm² cables to a grid switch and from that to 4 sockets labelled washing machine, tumble drier, fridge, and freezer follows the BS7671 without a problem we have worked out the load and also the chance of one cable having a greater share of the load to the other.

However to put any fixed item over 2kW on a ring final without considering how long it will run for and what the chances are of an overload is clearly wrong. In my house the fuse box is in the garage to tap into the ring final to run washing machine and tumble drier in the garage would likely cause an overload as so close to one end of the ring. Since fuse box is so close can't see why you would want to would be easy to run dedicated supply.

All the appendix says is we should consider what the load will do and should not simply plug it in without due consideration. We would not dream of plugging in the immersion heater to ring final and that has about the same demand as a tumble drier. Same with washer/drier. However with a simple washing machine, oven, dish washer although over 2kW the time is very short so not really a problem. The problem with the washing machine is other then the Bendix they were originally twin tubs and even the Bendix had hot and cold fill so they were not fixed we dragged them into the centre of kitchen on washing day. And the load was quite low. As time has gone on we have seen them use more and more electric power the heater no longer tops up the heat when you run out of hot water but is the only heat. However they also use a lot less water. Not in total but for each wash. The old machine we washed first whites, then colours and finally my overalls maybe three times so each lot of water had maybe 50 lbs of washing but not at the same time. Each item would go through the ringer into the spin dryer may be four times in a wash day. Before going on the line. It was very labour intensive. The gradual move has resulted in very little thought as to how the new washer/drier machines place as much as a demand as an immersion heater and can run for hours.
 
washing machines, dish washers, tumble dryers, even some ovens over 2KW come with moulded 13A plugs.
But when integrated over a long time cycle they are not necessarily 2kW loads.

What time cycle and what ratio of ON to OFF. ? The thermal mass of a copper conductor will absorb the heat generated from a short duration overload current that is many times the rating of the cable without the temperature of the copper rising more than a few degrees. But if the same over load current continues for a prolonged period then the constant rise in temperature will eventually raise the temperature of the copper to and above the melting point of the PVC insulation.

Of course in a properly designed installation the over current device ( MCB or fuse link ) will open before the cable starts to melt.. So maybe the situation of one leg of a ring final being "overloaded" if the entire 32 amp continuous load is close to one end of the ring is being over played. Would 2.5mm² copper carrying 32 amps for a prolonged period get hot enough to melt ( or otherwise compromise ) the PVC insulation ?.
 
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Would 2.5mm² copper carrying 32 amps for a prolonged period get hot enough to melt ( or otherwise compromise ) the PVC insulation ?.
If you're talking about Method C (CCC=27A) or Method E (free air, CCC=30A), then I'm quite sure that it wouldn't. It's a wild guess, but I'd be surprised if there would be a risk of 'melting' (I presume you mean the PVC, not the copper!) until one got to at least double the CCC, quite probably more.

Kind Regards, John
 

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