C172 Flight instructor and student reported burning wire fumes in the cockpit in the traffic pattern. Flight Instructor landed immediately and aircraft was towed to hangar.

Narrative

On Day 0 at around XA:45. My student and I went to go practice some takeoffs and landings. He is pre checkride for his private and was a brush up flight. We completed the walk around on the aircraft and taxi out to Runway XX as ZZZ was departing to the south and Runways YY/ZZ were closed. Our Runup was good and we continued for clearance to stay in the pattern which was right traffic for [Runway] XX. Our first takeoff and climb out was normal and we continued for the downwind for our first stop and go. On final we had a normal go around from another an aircraft in front of us landing which we didn't have a good distance between to continue. We continued for right traffic and tried again. Came into land and stopped on the runway. We then applied full power and started our takeoff roll. At around 700 feet AGL is when my student began to smell a strong burning wire smell and felt dizzy. At that point now we were at 1000 I had smelt it as well and now asked Tower if we could land and asked for a 180 back to Runway X as I knew the winds were calm. I opened the window on both his and my side to help with the smell and get some fresh air in the plane. I took controls of the aircraft and assured my student we would be just fine but just as a precaution and for both our safety I wanted to get on the ground. I briefed him and what I was doing and I asked Tower for a 180 to land on Runway X. I landed and asked Tower to exit Runway X to the left on [Taxiway] 1 shut the aircraft down and exited the aircraft where operations had met me and asked for my information. My student had calmed and felt a lot better on the ground as did I from the smell. The aircraft was towed back to our hanger facilities and was grounded by the school to review and see where it could have come from.