C172 Instructor Pilot reported the alternator drive belt failed in flight; causing the loss of electrical power. They ran the appropriate check list and performed an air turn back and precautionary landing.

Narrative

While exiting ZZZ and climbing to 4500 ft. on a training flight; my Student and I noticed the transponder turned off unprompted. After attempting to turn the transponder on; ZZZ departure notified us that we were broken over the radio. I restarted the radio twice; but the problem persisted and became worse until it became inoperative. I trouble shot the avionics by checking the circuit breakers; none of them had popped. I was unable to contact ATC or to squawk; lost comms as the radio and transponder were inoperative so I descended below 1900 ft. to remain clear of the airspace and began turning towards ZZZ1. When slowing down to land I noticed the flaps did not extend. This is when I suspected that there was an electrical failure. I had my Student read aloud the alternator failure checklist. Once that was completed I landed Runway XX at ZZZ1; taxied back to the Ramp and shut down the aircraft. Once on the Ground I called Tower informing them of what happened. Upon inspection the alternator belt had ripped and was no longer properly attached.