PA-28 Flight Instructor reported a complete electrical failure on initial climb that resulted in a loss of transponder; communications; all primary flight instruments; maps; and charts. With the help of the flight school's Chief Pilot for communication with ATC; the Flight Instructor landed safely.

Narrative

Total loss of electrical power in the air. Fuel on board during departure; 48 gallons - full tanks useable fuel. Starting the engine. At the beginning; noticed slight pop up of landing and strobe light circuit breaker; just a bit of white layer of circuit breakers could be seen and I; the instructor; put it back in. Noticed everything was fine and good to taxi. Run up. Noticed no issues with magneto check and voltage flow was well around 14V. During taxi and departure; Student Pilot hardly got his seat adjusted to reach out the controls and was showcasing macho; invulnerability; and anti-authority the entire time; who was also late for the flight but did not seem to care much. Hence the instructor was concentrating much on keeping the flight coordinated and safe the entire duration of flight. Takeoff from Runway XXR. Airspeed indicator came out alive/active and all indications on the systems were in green. Was asking the student to step on the rudder and get back to the centerline. Departed to north side. Climb. Noticed student repeating the same mistake; which was to keep his legs completely off the rudders; resulting in uncoordinated flight. Completed the climb checklist and verified. Cruise. Leveled the aircraft at 3;000 ft. and completed and verified the checklist. Slow flight dirty. Student completed the activity but drifted completely towards northeast since there was no rudder usage and interest to fly. While the flight was good and under control until now; we noticed the G750 turn off completely and the instructor concluded it might be overheating since the voltage was in green. Now we had lost our transponder; communications; all primary flight instruments and maps; as well as charts. Transitioning into approach stall. The student recovered in a very harsh way and we heard a loud bang closer to the engine. Simultaneously lost our G500 and G750. Hence; we lost all electrical power and flew with G5; which is our standby instrument. Noticed amps 0 in the systems and voltage dropping rapidly.Flight back to ZZZ. Took over the controls from the student; leveled off; and we were around 8 NM northeast of the field by then. Turned the aircraft around and stayed all the way clear of the approach paths of Runway XXR and XXL. Asked the student to help me with checklist and traffic sighting. Pointed the aircraft nose towards towers which is standard procedure to get back into the airport ZZZ. Maintained 3000 ft. MSL throughout. Contacted the flight school owner / Chief Pilot over the call and texts to clear the ZZZ airspace by stating I'll be circling on top of the runway between 2500 - 3000 ft. and come in land at Runway XXR and to inform the Tower the same instructions. Watched out for all the traffic for both runways and once I noticed all traffic holding their positions; I tried to circle around the Tower if we could notice light gun signals. Since it was bright and clear sky days; couldn't notice but received a text from the owner saying it's green we can come in a land. Following these instructions made a right descending turn on Runway XXR and made a safe landing. As soon as we landed the engine indications systems turned off as well. Left with only G5 standby instrument. The airport ground staff in a truck escorted us back to the Ramp.Noticed the alternator cable was cut. Maybe that was the loud bang we heard midair.