A C-172 CFI AND STUDENT AUTOMATICALLY RESET 1200 IN THEIR XPONDER DURING A FULL STOP LNDG AT HEF. UPON THEIR SUBSEQUENT CLOSED PATTERN DEP; PCT CALLED HEF REGARDING THE VIOLATION.

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I CONDUCTED A TRAINING FLT WITH A PVT PLT APPLICANT. I DEPARTED MANASSAS ARPT AFTER FILING A VFR ADIZ FLT PLAN IN AND OUT OF THE ADIZ SURROUNDING DCA. UPON RETURNING TO THE ARPT; I REQUESTED A 'CLOSE PATTERN' FOR LNDG PRACTICE. GND CTL INSTRUCTED US TO SQUAWK A CODE AND RPT MID FIELD ON EACH PATTERN. MEANTIME; THE STUDENT COMPLETED THE AFTER LNDG CHKLIST AND HAD SET 1200 ON THE XPONDER. WHEN WE TAXIED; WE EXPERIENCED EXTENDED DELAY; THE TWR RADAR WAS OTS. WHEN CLRED FOR TKOF; I FAILED TO SET THE NECESSARY CODE; WHILE INSTRUCTING THE STUDENT ON SHORT FIELD TECHNIQUES. I COMPLETED 2 CIRCUITS AROUND THE ARPT USING RWY 34L. BOTH INVOLVED TFC DELAYS. UPON COMPLETING THE SECOND LNDG; WE REQUESTED TO RETURN TO THE RAMP. GND CTL ASKED WHAT CODE WE WERE USING. OF COURSE I REPLIED '1200.' SHE ADVISED ME TO CALL POTOMAC APCH; AS WE 'HAD VIOLATED THE ADIZ.' I DID SO. THE SUPVR TOOK MY NAME AND CERTIFICATE AND ADVISED ME THE FSDO WOULD CONTACT ME. THIS WAS PLAINLY A SERIOUS OMISSION ON MY PART; ALTHOUGH UNINTENTIONAL. NO SAFETY ISSUES WERE INVOLVED. A MINOR FACTOR WAS INOP LOCAL RADAR. MY CORRECTIVE ACTION WILL BE TO ADVISE ALL MY STUDENTS TO NEVER SET 1200 IN THE XPONDER WHILE WITHIN AN ADIZ -- EVEN ON THE GND.