Like the name suggests, a strain gauge is a device used to measure the strain of an object. The devices electrical resistance varies in proportion to the amount of strain on the device.
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Strain gauge load cells are used to convert a force into an electric signal. There are other types of load cells such as hydraulic and pneumatic load cells.
I would recommend you use 1/0 gauge
16 gauge is rated at 13 amps, but I would use 14 gauge which is rated at 15 amps just to be safe.
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It depends on the load applied. With a load of 10 amps you would loose 5 volts at 100 feet. I would not run it over 50'. This is one of the reasons I never wire any home with AWG#14 wire even though you can use it in bedrooms. I prefer to use AWG #12.
14 gauge will handle it with a 15 amp breaker. If you use 12 gauge use a 20 amp breaker.