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I installed a junction box in my attic, i used 12/3 wire. I didn't need the 3rd red wire so I capped it off on both ends and just didn't use it. Everything works fine, but the red wire comes up positive when I test it with my multimeter. And I checked for continuity on the wires as well and everything is good. I don't understand how it's hot when it's not connected to anything and the wire isn't damaged anywhere or touching anything. I'm baffled.
 

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The neutral wire path down to the panel bleeds off the induced voltage so the result is zero as measured by yur meter.
o

If you have some electrical dexterity and skills you could connect a light fixture (a porcelain socket and some short wires will do) with incandescent lamp (bulb) across your meter probes while you measure the voltage from teh red wire to neutral. The minute phantom voltage will be bled through the light and you will no longer read a voltage on your meter.
 

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How come the neutral wire doesn't show up as hot then too?
The voltage only shows up on a high impedance wire while using a high impedance multi-meter. A disconnected wire at both ends represents a very high impedance open circuit. If it is in close proximity to a live wire it will receive an induced voltage due to the capacitance and inductance between the wires.

A neutral wire is not disconnected at both ends (we hope not anyway) so it is quite low in impedance (we also hope).

The last thing a homeowner needs is a high impedance digital multi-meter. A $10 analog one is much better for that kind of use. As an option, if you insist on digital, you can buy a digital multi-meter that provides a low inmedance (aka Low Z) switch selection for measuring these common type

For further reading, Google Mutual Inductance and Mutual Capacitance

Some meters to consider
 
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