Electronic – arduino – Will this wall wart supply enough power

About 1 billion percent. No useful work is being done except to heat your house, and energy is being dissipated which would not be dissipated if the wall wart was not plugged in. The actual quantity is small, so I wouldn't worry about it too much if you're concerned about your electricity bill - A few cell phone chargers left in the wall 24-7 won't make a dent. For some math, if a device is just barely CEC certified (0.5W no-load dissipation) and left in the wall unused all month, you have 730 hours (in one month) * 0.5W * 0.001 W/kW = 0.365kWh [kilowatt hours] and electricity costs of, say, $0.20/kWh, and you have a cost of $0.07 Find a dime, pay the bill. Compare that to, say, your 73W fridge, which will be around $10/month.

If, however, you have a lot of wall warts, or the small losses are significant to you, look at switch-mode power supplies. They're more expensive, but more efficient both at no-load conditions and during use, and switch-mode supplies will actually regulate, as opposed to transformer-based designs which require further regulation circuitry. You can tell what kind a converter is just by the weight - A switch-mode supply will have just a lightweight circuit board with some electronics inside, while a traditional wall wart has a big, heavy transformer. I've used CUI switch-mode PSUs before, they're a good company with a nice line-up: See this page for some of their AC-DC converter products. See their Compliance page for more information on efficiency ratings.

Note: Some people use the term "wall-wart" for the transformer-based devices only, while others use it for both switch-mode and transformer-based wall plug-in AC-DC converters.

Power out of wall-warts is solely determined by the load you connect to it and not by the potential power that can be fed from the AC wiring.

Say it's a battery charger and it charges 4 x 1.5V batteries at 100mA - power out of the charger = power into the batteries = 6V * 0.1A = 600mW.

AC power into the charger is 600mW plus some small residual power related to how efficient the wall-wart is. Typically 700mW to 1W.

Power output from 120Vac might be 20A * 120V to power a kettle = 2.4kW. It might be a lot more but it is the load or appliance that dictates power taken.

Things like this are made safe because wires are insulated and circuits are isolated. Output voltages are kept low so that the effect of electric shock is barely felt.

Same with current - current drawn by a circuit is as per the load circuit demands and there are protection devices that inhibit the current beyond the intended use of the wall-wart - not to protect the user (because the low voltage does that) but to stop the electronics inside frying when someone shorts the output.

Wall-warts usually have AC line fuses inside them to prevent faults devloping into fires.