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Are electrical wires Muktzeh? For example, I keep a few chargers for my mobile devices on my desk.
If so, what category of Muktzeh do they go under?
They are Muktzeh machmas Melucha just like batteries and telephones which are Ussor to play around with. They can be moved though if you need their place or if you need them for other uses. see OC siman 308 sif 3.