The range you actually have
The INA219 has four ranges and the INA3221 has one. Divide each by its board's resistor and the TK119 reaches 0.4 to 3.2 amps on 100 milliohms while the INA3221 reaches a fixed 3.28 on 50 — almost the same ceiling, by opposite routes, with steps eight times apart.
Millivolts, then amps
Neither chip has a current range. Both have a shunt voltage range, and the current range is what that becomes once you divide by the resistor fitted.
The INA219 has a gain stage in front of its converter with four settings, so four ranges: ±40, ±80, ±160 and ±320 millivolts. The INA3221 has no gain stage at all, and one fixed range of ±163.84 millivolts.
Divide the INA219's four by the TK119's 0.1 ohms and you have 0.4, 0.8, 1.6 and 3.2 amps. Divide the INA3221's one by its board's 0.05 ohms and you have 3.28 amps per channel — the number printed on the back of that board.
Why the INA3221 board has half the resistor
Put the INA3221 on the same 100 milliohms as the TK119 and it would stop at 1.64 amps. That is a narrow range for a board meant to watch three power rails, and the chip has no gain setting to widen it. So the resistor is what changes: at 50 milliohms the same ±163.84 millivolts spans ±3.28 amps.
Halving the resistor halves the millivolts for every milliamp, and that has a price. The INA3221 counts in 40 microvolt steps, so across 50 milliohms one count is 0.8 milliamps — eight times coarser than the TK119's 0.1. Its fixed zero-point error doubles in milliamps for the same reason.
The result is two boards with almost the same ceiling, reached in opposite ways: the TK119 by stretching the chip's input, the INA3221 by shrinking the resistor.
What the gain setting does not change
It is tempting to read "narrower range" as "more decimal places". It is not.
The INA219's shunt register counts in 10 microvolt steps at every gain setting — TI says so in the register section, not only in the summary table — so one count is 0.1 milliamps whichever of the four you choose. Changing the gain moves where the reading saturates and nothing else about the resolution.
What it does change is the zero-point error, and that is worth knowing: TI quotes ±100 microvolts of offset at ÷1 and ±200 microvolts at ÷8 for the A-grade part fitted here. Across 100 milliohms that is ±1 mA against ±2 mA. So the narrow setting is the accurate one, and picking the widest range "just in case" costs you a milliamp of truth at the bottom of the scale.
Past full scale
On either board, a current beyond the range does not raise an error. The reading sits at full scale and stops moving, which looks like a perfectly steady load, and there is no flag in any register that says so. If a number is pinned at 3.2 or 3.28 amps, assume it is saturated rather than steady.
And the resolution neither board has
One count is 0.1 mA on the TK119 and 0.8 mA on the INA3221, and the fixed offset is a few counts wide on both. A sleeping ESP32 draws tens of microamps, which is less than one count on the better of the two — and buried under an offset ten times that size.
These boards watch a rail at work. They do not measure sleep current, and no setting makes them — that is a job for a meter with a microamp range, or for the way the ESP32 book measures it.
When it does not work
It has saturated. Each range has a full-scale current, and above it the shunt register pins at its maximum and stays there while the real current carries on climbing. On the INA219 pick a wider gain setting; on the INA3221 there is no wider setting, so 3.28 A per channel is the end. Nothing is damaged by going a little past it — at 3.28 A the INA3221's 50 mΩ resistor dissipates about half a watt — but the number has stopped being a measurement.
Your sketch or library is dividing by 0.1 Ω, and the board has 0.05 Ω. An example written for a different INA3221 board, or a library's default, may well assume 100 mΩ. Set the shunt to 0.05 in the sketch and the current doubles into agreement — and the 3.28 A printed on the back of the board is the range you then have.
It would not: the shunt register counts in 10 µV steps at every gain setting on the INA219, so one count is 0.1 mA whichever you pick. What a narrower range buys is accuracy rather than resolution — TI quotes ±100 µV of zero-point error at ÷1 against ±200 µV at ÷8, so the same reading is twice as trustworthy at the narrow end.
More than it can measure. The TK119's shunt is rated 2 W, so it is inside its rating up to about 4.4 A and dissipates around a watt at 3.2 A — hot to the touch but fine. The INA3221's 50 mΩ resistors run cooler for the same current, about half a watt at 3.28 A. 5 mm screw terminals of this size are normally rated for several times that. The limit you meet first is the chip's range, which is the safe way round for it to be.
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