How to connect wires if the distribution box is too short
If you have an electrical box with wiring that is too short to make electrical connections to outlets, switches or even another junction box, you will need to add 'pigtails' to the wiring in order to lengthen the wiring so you can use it. In this video I show you numerous ways to fix wires that are too short in an electrical box. I know that the general tactic for extending wires is using a J-Box, but it's against code to leave a J-Box in a location that's inaccessible without cutting drywall. I would use a 4-11/16 deep box, unless you're sure you'll only have 2 of these, then a 4" x 4" x 2-1/8" box will suffice.
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