I have been analyzing various datasheets of current sensors and majorly getting sensitivity given in "mV/A," from which I understand the output voltage per 1 ampere. I do not understand it when sensitivity is given in "mV/N" and "mV/mT".
Sample snaps:
How can we understand this?
The first one is using units that are a bit sloppy. It should be \$\frac{mV}{A\cdot N}\$ where N is the (dimensionless) number of turns through the core. So mV/A is the number given multiplied by the number of turns.
The second one specifies sensitivity in terms of the magnetic field created by the (external) conductor. Magnetic field is measured here in milliteslas (mT). Named after the Serbian inventor Nikola Tesla. That's perhaps less satisfactory in the intended application since it does not really guarantee the output in terms of current flowing through the conductor. The datasheet should give direction in predicting the B field from the conductor in terms of mT/A.
[...]sensitivity is given in "mV/N" and "mV/mT".
Not "mV/N" but \$ (mV\times N)\$, where \$ N\$ is number of turns. This refers to a current transformer where transformer iron or ferrite confines magnetic lines so that a primary winding (usually one-turn) links almost entirely to multiple secondary turns.
Every secondary turn is similarly linked, so that voltage generated is multiplied by number-of-turns. This is often expressed as "Ampere-Turns".
In the case of OP's sensor, the number of secondary turns is fixed (because the secondary turns are potted into the sensor body). But you are free to add as many primary turns of the wire you wish to monitor.
For example, winding a current-carrying-wire so that it passes 3-times through the sensor hole will result in triple output AC voltage. The three turns must carry current through the hole in the same direction - of course current must be alternating in direction, but at any instant direction must be the same.
