Does a higher gauge electrical wire impact voltage level?

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@jasonbourne52

Not sure how.

V(dropped) = I(current) * R.

Under load, thicker gauge wiring has lower R for the same length and current.

OP : Yes, wire gauge can (in theory) impact voltage at the load.   A perfect wire has no voltage difference, and would have the same voltage at the load as at the source, whether we are talking AC power or speakers.

In AC power transmission in a home, 1-2 V per leg loss is normal.  Meaning, 2-4 V drop at the appliance relative to the panel.  A higher gauge wire than required can reduce this. 

As I mentioned before, the voltage loss (i.e. drop) is proportional to the current.  It is also proportional to the wire length.  For the same wiring, a high current device on the end of a long line will suffer more drop vs. a low current or short run.

For speaker cables it is extremely rare to expect voltage drops more than a couple of tenths of volts with anything equal to or better than 14 gauge cables.

Speaker cables? Got anything else extraneous to the OP?

Wire gauge will not affect no-load voltage.  Your reported voltage swings are very large and do not reflect well on your local utility's ability to provide you reliable source of electricity.

Voltage swings like this are likely accompanied by other imperfections such as noise. 

You are a prime candidate for a power regeneration (rectification/inversion) unit. 

@jasonbourne52  Erik's statement is correct.  Lower gauge wire has a higher number.  So if I have a number 12 wire and want to go to a higher gauge, I will go to a 10, not a 14.