I have the practice of keeping cords of all types with their devices. Power cords, USB cords, VGA cords, each one is assigned to its own device.
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If you assign the power cord to the device then it does not matter if the cord is weak as long as it is good enough for the device.
Yes that is a good idea! As you can see from this example, even though the power cord is marginal and has fake information on it, for the specific use intended (used with this particular power adapter that is made for the hard disks) it is suitable. The power adapter doesn't make use of the ground anyways, so that it doesn't matter that the cord doesn't have one. And the current rating on the power supply says it is < 1A, again well within the miniscule amount of copper in those 2 conductors.
I just don't like that they chose to use the "format" of a normal 3-conductor power cord that fits the IEC C13 connector, and then decided to fake the label on it (or use one from a faked supplier). Many people would not follow your practice of keeping cords with the devices they come from. That is a wise move!
But most people might just "bin" the extra cords (like I do) into a scrap bin... and then when I need to use it for something, grab it and plug it in. That's not going to happen anymore! I've learned my lesson! Especially since it uses a C13 connector which is widely used on many other devices, and I have lots of legitimate C13 power cords, I never thought to check. Now I'll have to.
Look at all of these other connector types they could have used:
I'm not sure if these would be any better, but for example if they used something like a C7, they are not grounded so right away that would eliminate one possible misuse. Second, perhaps they pick one typically used on smaller devices so even if someone decides to re-purpose the cord, it will go into something that doesn't draw much power (like a little portable radio, calculator or something like that). Now I'm making excuses for them... but there is no excuse. Maybe they have in the factory a machine that churns out IEC C13 type 3-prong power cords by the millions... and it is the cheapest possible option if all they change is the wire, it is cheaper than if they try to re-tool the machine to make other type ends? No, another excuse... I can't come up with any legitimate reason here. Cheapness of the power cord contents I understand... but the terminal ENDS of the cord I still don't get why they chose IEC C13 type with a ground connection when it is useless. Seems like it would cost more to do that than using 2-prong ends.