My bad on the scaling. I corrected it.
Assume a transducer with a 0 to 5 volt output. So 0 to full scale transducer becomes 0 to 1024 bits (2^10). Therefore not even considering any other error since 0 to 1024 bits is 0 to 5 volts we can take 5 volts and divide by 1024 bits and get 0.00488 volts per step change. So we can call it at 4.88 mV being the best resolution we can get with a 10 bit ADC conversion.
That in mind if we use a transducer to convert current to a voltage it works out this way in this case. The current transducer converts 0 to 250 amps to a nice useable 0 to 5 volts. Therefore the transducer output becomes 5 / 250 = 0.020 or 20 mV/Amp. So with a 10 bit ADC our best resolution will be about 4.0 amps or 20 / 4.88 = about 4.098 Amps.
That is what I was getting at and that assumes no other error. That assumes a perfect 5 volt reference on the 10 bit ADC.
Now back a little I mentioned along with using a current transformer the importance of knowing that we can't just use any resistor for a burden resistor. I provided a link explaining that. This comes down to:
What is Burden?
The load, or burden, in a CT metering circuit is the (largely resistive) impedance connected to the secondary winding. Typical burden ratings for IEC CTs are 1.5 VA, 3 VA, 5 VA, 10 VA, 15 VA, 20 VA, 30 VA, 45 VA & 60 VA. ANSI/IEEE burden ratings are B-0.1, B-0.2, B-0.5, B-1.0, B-2.0 and B-4.0. This means a CT with a burden rating of B-0.2 can tolerate up to 0.2 Ohms of impedance in the metering circuit before its output current is no longer a fixed ratio to the primary current. Items that contribute to the burden of a current measurement circuit are switch-blocks, meters and lenghty secondary conductors.
The most common source of excess burden in a current measurement circuit is the conductor between the meter and the CT. Often, substation meters are located significant distances from the meter cabinets and the excessive length of small gauge conductor creates a large resistance. This problem can be solved by using a larger gauge secondary wire, or a CT with 1 ampere secondary which will produce less voltage drop between a CT and its metering devices (used for remote measurement).
The above was taken from here.
Something I overlooked and forgot to mention is what JohnRob was kind enough to point out. Do not leave the secondary of a current transformer open. either short it or have a burden resistor across it.