Or can they run anything that runs off USB e.g. a small desk-light or fan?
I’ve got one which is failing to run a LED lamp, not sure if it’s the unit or just the way they work.
Not a really satisfying answer, but it’ll depend on the model and the device.
Some power banks should be able to power a small desk light or fan. It’ll depend on how much current the device needs and how much the power bank is designed to provide. The USB port itself should provide 5V. If it’s USB 1 or 2, it’ll support 500mA. USB 3 up to 900mA. If you have a USB 2 compatible power bank but the lamp expects more than 500mA, it won’t work, even if it’s a working power bank. There are also some with multiple ports, some of which provide different amounts of max current.
Edit: Also, it’s possible to design a power bank to be out of spec and supply a USB port with more than 900mA and/or for a device to expect more than that, which is also a possibility. I would not be shocked by a fairly powerful desk lamp that wants to draw 1 or 2 Amps.
My experience is that they will power anything that runs off of USB.
Missed the edit window, but for example, a 10W lamp would mean it draws 2A (5V * 2 Amps = 10W). And a 10W LED light is not example uncommon or unusual. So, it might have a USB style connector for power but needs to be plugged into the wall instead of a power bank, which probably isn’t designed to handle that kind of load.
As I noted, it will depend on the specs of both power bank and device.
The problem can actually be the opposite of what is mentioned above (the draw is too high), but rather that the power draw is too low. Most USB batteries will turn off if too little or no current is being pulled from them.
If it is a small LED lamp that is designed to connect to a computer or USB hub, then it will certainly draw less than 500mA. A random search found a $10 one with 8 LEDs that is claimed to draw 165mA. The shutdown current for some batteries I found is 30mA. So, if the OP’s light used just one of the LEDs from that lamp, the battery would not stay on.
People use (good quality) USB power banks to run Raspberry Pis for modest intervals. The really gonzo folk go for ones with 20000mAh capacity!
The load of a “doing anything at all” Pi is enough to keep the bank from shutting off. Until it runs low when it just switches off without a clean shutdown.
Thanks, this appears to be the case after a bit of testing. The powerbank has an LED display to show its own situation, and I observed that the display and the USB lamp both go off simultaneously after about half a minute - and the display goes off on its own in the same period if nothing is plugged in. lol LED efficiency turns frustrating