C172 TRAINING FLT GETS TAGGED FOR A DC ADIZ VIOLATION WHEN THE 2 PLTS FAIL TO SET THE XPONDER TO ALT AFTER ENTERING THE CODE AS RECEIVED FROM THE MIL TWR AT NYG.

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MY STUDENT AND I HAD BEEN MANEUVERING SW OF BROOKE VOR. WE WERE READY TO RETURN TO QUANTICO MCAF. APPROX 4 MI SW OF BROOKE VOR; MY STUDENT CALLED QUANTICO TWR AND PICKED UP OUR SQUAWK CODE TO RETURN TO QUANTICO OF XXYY. QUANTICO TWR TOLD US TO RPT BUD'S FERRY. WHILE WE WERE STILL SW OF BROOKE VOR; MY STUDENT TURNED THE XPONDER TO STANDBY AND SET THE XPONDER CODE TO XXYY. AT QUANTICO; WE CONDUCTED A FLT SCREEN PROGRAM (IFS) UNDER CONTRACT TO THE UNITED STATED MIL. THE MIL IS VERY STRINGENT WITH THE FLT HRS ALLOWED; SO EVERY SECOND OF EVERY FLT MUST BE UTILIZED TO THE MAX EXTENT POSSIBLE. MY STUDENT IS AN IFS STUDENT. I HAD MY STUDENT CONTINUE TO PRACTICE MANEUVERING AT DIFFERENT AIRSPDS ENRTE FROM SW OF BROOKE VOR TO BUD'S FERRY. MY DISTR WITH ENSURING THAT NOT A SECOND OF FLT TIME WAS WASTED AND THAT THE SYLLABUS WAS ADHERED TO PRECISELY FOR THAT FLT DEFINITELY CONTRIBUTED TO MY MISSING THE FACT THAT MY STUDENT HAD NOT RESET THE XPONDER TO ALT AFTER ENTERING THE XXYY CODE. APPROX 5 MI S OF QUANTICO MCAF; I NOTICED THE XPONDER WAS STILL ON STANDBY. I IMMEDIATELY TURNED THE XPONDER TO ALT. WHEN MY STUDENT RPTED BUD'S FERRY; QUANTICO TWR TOLD ME TO CALL POTOMAC APCH AS SOON AS WE LANDED. TWR SAID THEY THOUGHT IT HAS TO DO WITH POTOMAC APCH NOT RECEIVING OUR SQUAWK PART WAY TO QUANTICO BECAUSE POTOMAC APCH HAD CALLED THEM AND ASKED THEM IF THEY WERE TALKING TO US. TWR ALSO ADVISED US THAT THEIR RADAR WAS DOWN; SO THEY DID NOT KNOW THERE WAS A PROB WITH THE SQUAWK UNTIL POTOMAC APCH CALLED THEM. AS SOON AS WE REACHED THE RAMP; I CALLED POTOMAC APCH. THE PERSON WHO ANSWERED THE PHONE IDENTED HIMSELF AS MR X. HE INITIALLY SAID I HAD BEEN SQUAWKING 1200 IN THE ADIZ. I TOLD HIM THAT THE XPONDER HAD BEEN ACCIDENTALLY LEFT ON STANDBY WHEN WE ENTERED THE ADIZ AND THAT AS SOON AS I DISCOVERED IT; I HAD TURNED THE XPONDER TO ALT. WHEN I ASKED HIM HOW A XPONDER SET TO XXYY COULD SQUAWK 1200; HE CHANGED HIS STATEMENT TO SAY THAT POTOMAC APCH; CUSTOMS RADAR; AND THE AIR DEFENSE RADAR; ALL AGREED THEY WERE SEEING A PRIMARY RETURN FROM MY ACFT. MR X SAID HE HAD TO CONDUCT A PRELIMINARY INVESTIGATION. IN THE FUTURE; I WILL ASK THE CTLING ATC FACILITY TO VERIFY THEY ARE RECEIVING MY SQUAWK BEFORE ENTERING THE ADIZ. I WILL SUPERVISE ALL MY STUDENTS' OP OF THE XPONDER MORE DILIGENTLY.