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Adafruit_ADS1X15
Driver for TI's ADS1015: 12-bit Differential or Single-Ended ADC with PGA and Comparator
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InfluxDB
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How you do the code will depend on which library you use for the ADS1115. I didn't see anything brain-damaged in the Adafruit library, so it should work for you. I'd run it in single-shot mode, since you'll be scanning the 4 inputs; it only runs continuous mode on a single channel. Their Doxygen doc sucks... look at the single-ended example instead. It's dead simple to use. A gain of 4 or 8 is your best range, then simply multiply the result by 10 (because of the 0,1 ohm resistor) and you'll have the current.