alternator wiring questtion

[Rich <emt@imcnyc.com>]

I see 2 wires hooked up to my alternator on my 87 2.0 16v.
the top wire is thick  and runs to the starter which then runs to battery positive post.  (power is my logical guess)

MY QUESTION:   there is a skinny wire, directly below the thick wire, that connects to a small screww and leads to gosh nows where.  This skinny wire is not in the best condition.
What is this lower wire?
Is it important/ vital for proper functioning of car?  
What does it do?
Where does it lead to?
What is its function?

Is it easy to replace?
What guage wire should I use?

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