What are possible causes for the flaps not deploying on a Cessna 172? I would like to seek some expert opinion on why my flaps failed to deploy when I took it to Flaps 20. 

I was turning from Downwind to Base when I took flaps 20 and noticed that my speed was creeping past 80kts even at idle power. My instructor took a look outside and that’s when we realised that the flaps were still at the UP position. We tried checking the circuit breaker for Flaps and the other switches, and everything else was normal. 

We came in flapless until short finals when the flaps deployed to Flaps 10 when the switch was moved to the Flaps 30 position. 

We did some checks on the ground and whenever we took Flaps down, static interference could be heard. It’s as if it was timed to happen the moment the flaps are extended. No static heard when the flaps are raised.

Any expert opinion would be appreciated as I would like to really understand what I am flying. I have checked the POH and it barely says anything, even the Electrics diagrams aren’t helping me diagnose why. 

I’m a student pilot with barely 20 hours flight time.
If the flap actuating motor is defective, you'll get exactly (or very close to) those symptoms, including the "interference" when the motor is operated. It could also be that the power connector to the motor was loose, damaged or corroded.