The current transformer should measure down to zero current. Don't know why it says 1-10A.
If you are converting the AC from the transformer to DC for measurement then you may need to use an op amp configured as a precision rectifier to maintain linearity below 1A.
AC current 0-10A 240V single phase. I need a sensitivity of 5mV/5mA.
1 ohm resistor can do this sensitivity needs to have a wattage of 100W while the current transformers at my place here are not practical in my applications. I'm stucked.
I have some CoilCraft CS60-010 transformers.
At 10A they read about 10% low.
At 3A 0% off.
At 1A +10% off.
This is because of the resistance of the very small wire in the transformer.
I think the 1A rating is only because of the +10% error. I need to think about it, or try one, but my first thought is that it will be +20% at 0.01A.