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Serious Thumper
   
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Savage heart of darkness
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Well, you're mostly right. Usually it depends on how much power the device requires and/or how long it is expected to operate without power (outage)? For instance, emergency lighting may require substantial power, but may only need to run for 20 minutes until everyone has exited. If your device is a tiny nano power type gadget that runs for years on a 2032 coin type power cell, then there's no need to rig a charging system. On the other hand, if it's a lighting, noise making, or motorized device then it probably requires larger AAA or AA cell power, and rechargeables might make sense.
Most engineering projects go thru 4 distinct phases...
1) a clear problem definition (don't underestimate this; it sets your starting point for the rest of your solution)
2) a proposed solution with goals it will solve & achieve (i.e., a gadget)
3) a REQUIREMENTS phase where you decide the physical dimensions, power requirements, color, noise level, etc.
4) the DESIGN phase where you build one or more prototypes that meet or exceed the REQUIREMENTS you have defined. These units are used for testing. If they fail, then you may to restart step 4 or even go back to step 3 and rethink the project from a different approach. Note, this is called empirical scientific method.
Keep in mind if you're applying AC directly to this gadget (rather than using a DC wall PS) it could be LETHAL! Most power supplies use a small transformer which steps down the voltage, but also electrically isolates the circuit from the AC line. You can apply direct AC (rectified, of course) to a circuit, but it can be tricky and DANGEROUS if you don't have a good understanding of AC/DC principles.
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