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However, if you increase the voltage, add a wall power adapter, ...
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Oh give me a break! I go on vacation and look what happens!
Wall power adapters ("wall warts") are inherently energy-limited, just like batteries. They have a low output impedance that is better than batteries. They are indescribably safe, just like batteries.
And you can use one that is inappropriate for the application to the point of being dangerous - JUST LIKE BATTERIES.