2006 Jeep Liberty - wire connection?

were does the small wire from positive terminal connect in the back of the jeep–just hanging down

How about a little more info?

Did you get the jeep as a pre-owned vehicle?
Is it possible to post a photo of dangling wire?

What color is the wire? Any colored stripes? Any connector/terminal?

In the back of the Jeep?
Where in the back? Luggage area? Rear passenger area? Tail light area? Under rear bumper? Near a trailer hitch?

How do you know it’s from a positive terminal? Did you test it?
CSA
:palm_tree::sunglasses::palm_tree:

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I’m going to guess that the wire is is the small wire at the terminal that connects to the Positive battery terminal.

If that is the one, it should follow to a fusible link that runs to the back of the alternator.
This wire is where the current flows back to the battery to charge it.

Yosemite