[stuarth]

Once you’ve adjusted the reference current to give zero volts across the resistor, there is of course zero current in the resistor.

Think of two current loops, one carrying the unknown current, the other carrying the reference current. Then break both loops and reconnect them via a shared resistor, to make a circuit with two conjoined loops.

Now consider the unknown current flowing towards the resistor, but getting diverted through the reference current loop. Because the reference current is adjusted until there is zero volts across the resistor, you’ve effectively added a zero resistance ammeter in the path to the unknown current.

Stuart