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I have stripped one wire, the black/hot/positive one, for a 120v appliance. I had to cut away the outer plastic that surrouneds all three wires, and now I'm afraid I may have nicked a small hole into one or more of the wires, and am deathly afraid of getting shocked.

Is there a way to test for very small holes in wires? The ole put-water-on-something-inflatable-and-listen/feel-for-bubbles comes to mind, but this is electronics. I suppose I could closely inspect the wires, but am hoping there's a better way.

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Just wrap it with an electric tape.. Or cut it shorter. – Eugene Sh. Jan 11 at 18:15
    
How reliable is electric tape? I believe I read to wrap it as thick as the wire. Is that right? – JohnAllen Jan 11 at 18:20
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That is exactly what electrical tape is made for. Wrapping it as thick as the wire is beyond excessive. 4 or 5 layers will do. – Matt Young Jan 11 at 18:26
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Some of the answers mention bending or wiggling the wire to find any nicks. This is good advice, but please realize that they aren't talking about severe bends. You just need to put a 10-15-degree curve in the wire which will "stretch open" any nicks and make them more visible. If, instead, you bend the wire sharply back and forth, then it will quickly become brittle and break. Try it with a paper clip to see what I mean :) – bitsmack Jan 11 at 20:49

Plastic insulation for the mains is quite thick so any damage has to be pretty macroscopic to cause danger. Electrons won't come spilling out of a pinhole like water from a punctured tube (at least at mains potential).

Just inspect it thoroughly, bending it back and forth and look for any cracks or any visible copper. If you find some, shorten the cord to eliminate it. If you think you might have damaged the cord in some particular place, you may be able to just remove that end and shorten it a bit.

I could tell you to dunk it into saline solution and check the resistance but I think that would be a terrible idea. Or you could connect it to a 25kV+ source and observe it in a dark room looking for a purple corona discharge (an even more terrible idea).

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The problem with nicking the wire is that you have caused mechanical damage. This isn't going to be a problem in the near term, but in the future as you wiggle the wire around\pull on it, it can cause a point of strain and break. When manufacturing cables this can be a problem, and especially aerospace industries take great care in avoiding it. Even inspecting pins after stripping with a microscope and having people sign off on it before they will put the pin in the housing. You'll probably be fine if you haven't cut through to the copper or cut through more than 20% of the insulation. If you have, try and find the point where you though you nicked it and wiggle it until you see the break, then electrical tape it tightly to give it strain relief. If your worried about it for safety's sake, just replace the whole cable.

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Essentially you want to break the small holes out to a larger area. Its not safe, but you are lookin for something along the lines of drape the cable through water (not the end). Then measure the water for a voltage. If you have a voltage, then you have a hole... I don't think you should mess with this, as it is dangerous, but I just wanted to answer your question. A Eugene Sh. had a much better suggestion of electrical tape.

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