PLT OF C182 INADVERTENTLY CHANGES SQUAWK TO VFR WHILE IN DC ADIZ.

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WHILE FLYING A C182 SKYLANE; I INADVERTENTLY COMMITTED AN ADIZ VIOLATION. I WAS PIC; GIVING A PROFICIENCY CHK TO ANOTHER PLT. WE DEPARTED FREEWAY (W00) TO GO TO THE MARYLAND EASTERN SHORE PRACTICE AREA. FREEWAY IS LOCATED IN THE WASHINGTON DC AIR DEFENSE IDENT ZONE. UPON DEPARTING FREEWAY; WE WERE SQUAWKING OUR ASSIGNED DISCRETE CODE; XYZW. WE ESTABLISHED RADAR AND RADIO CONTACT WITH POTOMAC TRACON AND WERE TOLD TO PROCEED. AFTER SEVERAL MINS ENRTE; ABOUT 6-8 MI E OF FREEWAY; THE CTLR GAVE A FREQ CHANGE. THE NEW CTLR IMMEDIATELY GAVE US ANOTHER FREQ CHANGE. THE THIRD CTLR ASKED FOR AN IDENT AND FOR US TO STATE OUR POS. I THEN NOTICED THAT THE XPONDER WAS SQUAWKING 1200 (VFR). I IMMEDIATELY RESET IT TO OUR DISCRETE CODE. SOON THEREAFTER; THE CTLR QUESTIONED US AS TO WHETHER WE HAD BEEN SQUAWKING VFR EARLIER. WE ADVISED 'AFFIRMATIVE;' STATING THAT WE HAD A XPONDER PROB. HE THEN GAVE US A TELEPHONE NUMBER TO CALL WHEN WE GOT ON THE GND. WE LANDED AT EASTON (ESN) AND I CALLED THE NUMBER AND ANSWERED A LIST OF QUESTIONS. HERE'S WHAT I THINK HAPPENED! THIS ACFT HAS A COMMERCIAL VENDOR XPONDER. THIS XPONDER HAS A 'VFR' BUTTON ON ITS PANEL THAT; WHEN PUSHED; RESETS THE CODE TO 1200. APPARENTLY; I SOMEHOW BUMPED THAT BUTTON THEREBY RESETTING THE XPONDER CODE TO 1200. ANOTHER POSSIBILITY IS THAT I PUSHED THE 'VFR' BUTTON WHEN ASKED TO IDENT.