AC/DC wattage conversion

Question

I've got some common Dutch "huishoudsnoer" (household-cable? Mainly used for powering lamps. Not solid core, 2*0.75mm² cable) laying around, that's rated for 1380 watts. Our wall sockets provide 230V at 50 hertz, so 1380 watts is 6 amps.

I've got a 3d printer, on which I want to change the power supply. The current one is 21 amps at 12V DC, or 252 watts. Way less than 1380 watts.

Am I safe using the cable I've got laying around, or is there some magic involving DC and AC? If so, how do I calculate how much DC power a cable can carry, given a certain AC capacity?

Answer 1

When it comes to cables delivering power, then it is the current that is the most important. Or rather, easiest to calculate with. This is because power across a component is resistance times current squared.

Your household-cable is rated for 6 A AC. This value is in RMS (Root mean square) value. So no conversion is required, it's equal to 6 A DC.

So no. You cannot use one of your cables to supply all that current. You can however put several cables in parallel, namely \$\frac{21 A}{6 A}=3.5 \rightarrow 4\$. If I were you I would add a couple more to add some margin, so say 5 or 6.

You can do it with at least 4 of those household-cables in parallel. It would certainly work. Though I'd recommend getting some other cable rated for 21 A, because it will look more professional + take less space because you won't have as much plastic around the cable.

Answer 2

Am I safe using the cable I've got laying around,

Nope.

or is there some magic involving DC and AC?

It's not an AC vs. DC problem. It's that the thing that determines whether a cable is suitable for the job has much more to do with the current flow than the power. So you almost don't want to pay attention to the power being conveyed, and only pay attention to the current being carried.

Things get a bit complicated with cables, because you're partially worried about the voltage drop in the cable, because that voltage drop means lost power, and you're partially worried about the cable heating up and catching on fire. The cable heat problem gets even more complicated because a bunch of conductors in a bundle can't dissipate as much heat as a single conductor in free air, so the middle of the bundle may get too hot.

The bottom line is that you need heavier gauge wire. Secondarily, you can probably get away with insulation that's rated for a much lower voltage than your "household cable" (which, I suspect, has insulation that's good for 600V or more, if the European authorities are as conservative as I expect them to be with house wiring).

I'm not sure about Europe, or if huishoudsnoer is the cable you find inside the walls (as opposed to lamp cords). In North America the typical house wiring is solid; inside of devices people generally go with stranded wire so that ordinary motion and vibration don't break things.

Around here the best place to get stranded wire that's good for carrying that much current in a 12V environment is the local auto parts store. Some places even label the packaging with the current-carrying capacity. If you don't want to do that, then you need to order some from whoever is the usual suspects over there.

Note that the stuff that's good for cars is not what you'd want to use going to the print head, or anywhere else that the wire is being bent all the time -- that requires special wire (called "continuous flex" in English) that uses extra-fine strands, a special alloy of copper, and special insulation, all so that the wire can be in constant motion without breaking.

Answer 3

The cable label is intended to give the consumer an easy way to check that the maximum rating is not exceeded by adding up the power consumption (watts) of all the devices plugged into it at the expected mains voltage. The manufacturer will have taken two factors into consideration:

• The current, which will cause some heating of the cable.
• The length, which will determine the voltage drop at maximum load at the load end of the cable.

At 6 A rating it is probably only a 0.75 mm² conductor and this will get rather warm at 21 A. I would recommend that you increase or double-up to at least 1.5 mm² and 2.5 mm², if you can.

You can play around with an online cable resistance calculator such as Chemandy's (picked at random) to get a feel for what's going to happen. With the result you can then calculate the voltage drop along the cable at 21 A (IR) and the power dissipated in the cable (I²R).