Generating AC current from microcontroller
you're driving the primary resistance secondary resistance and the burden resistor all effectively in series. (the 1:1 ratio greatly simplifies the impedance transform) so your driver needs to produce sufficient voltage on the primary terminals to drive the needed current through that resistance.

An audio amplifier chip might be suitable where you draw the op-amp.

you're going to need to isolate the primary when you want to measure real-world currents. so you may need a relay in the circuit too.