How does an inductor behave if we try to operate it beyond its self resonant frequency?

 

It operates more like a capacitor.

Bob

 

Self Resonance -

https://wiki.analog.com/university/courses/electronics/comms-lab-isr


Regards, Dana.

 

It becomes a capacitor that can't block DC.

 

The capacitor is the stray capacitance from the inductor windings that appears to be in parallel with the inductance.
The self-resonant frequency is when the inductive reactance equals the capacitive reactance, of course.
Above that frequency the capacitive reactance becomes dominant.