Thanks for all the info, installed a brass shim and took care of the issue.  Had tried many other things like looking for bad ground and making sure all other connections were tight, but the shim worked and cost me $3.50 at ace hardware.  Went with a 0.064" thick and 0.5 wide piece cut to size (about 1-inch long), drilled proper holes to fit over brass bolts, placed above the first set of nuts, reassembled per specs (steel washer, copper lock washer, brass nut).  Started car and it fell right on + of the zero mark and not a bounce.

Original Post

Glad it worked. Montana. Note that the gauge now reads a proportion of the amperage rather than true reading, due to the increase in conducting area from the shim. But when I did it in the last century, I figured that I couldn't get a stable reading as-stock anyway, so....

Was also wondering if I use a thinner brass shim, will the current going through the Amp meter increase and give a truer reading while also reducing the bounce?

AFAIK, electrical conduction is dependent on the surface area of the conductor. This is why braided wire works better than solid wire as the surface area of all those little strands vastly increases the conduction. I suspect that if you decrease the area of the jumper-shim very much, the gauge's needle-flutter will return. To me, amp gauges are much like a go-no-go gauge or idiot-light: current is either flowing forward (+) or back (-), so things are working (or not). Exactly how much current is flowing is far less less important than the fact that some is flowing and in the correct direction. But I'm no expert.

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