AN SF34 CREW; DEPARTING DFW; RESPONDED TO A DSND RA FROM TCASII.

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AS WE WERE APCHING 3000 FT; CLBING OUT OF DFW; WE RECEIVED A TCASII RA TO DSND. I ASKED FO TO RESPOND TO RA; AS I TRIED TO ASK DEP CTL IF HE SHOWED ANY CONFLICTING TFC. THIS RA WAS VERY UNUSUAL; IN THAT ATC SAID THERE WAS NO CONFLICTING TFC (ONCE I WAS ABLE TO COMMUNICATE ON CONGESTED FREQ). ALSO; THE RA CONTINUED EVEN THOUGH WE HAD DSNDED ABOUT 800 FT. SO; I ASKED FO TO ABANDON RESPONDING TO RA AND RESUME CLB. I RECYCLED TCASII SWITCH TO STAND-BY AND BACK TO AUTO; THIS DISCONTINUED THE RA COMMAND. APPARENTLY; THIS WAS A SPURIOUS TCASII RA. SINCE WE ARE TRAINED TO RESPOND TO RA'S AND NOT TRY TO SECOND-GUESS THE VERACITY OF EVERY RA; WE RESPONDED. IN RETROSPECT; THIS MANEUVER TURNED OUT TO BE A HARROWING EXPERIENCE FOR THE PAX. HOWEVER; THE ALTERNATIVE OF NOT RESPONDING TO THIS RA; AT ALL; THEN FINDING OUT THAT IT WAS A GENUINE RA; MAY HAVE BEEN EVEN MORE HARROWING; IF NOT WORSE! A FEW MINS LATER INTO OUR CLB; WE NOTICED A TRANSIENT ANOMALY IN THE BACKUP CHANNEL OF THE ACFT'S WARNING ELECTRONIC UNIT. IMMEDIATELY; WE CONTACTED COMPANY MAINT. CONSENSUS WAS REACHED TO RETURN BACK TO DFW ARPT. THE REST OF THE FLT WAS UNEVENTFUL. ALSO; THE WARNING ELECTRONIC UNIT REDUNDANCY LIGHT NEVER REILLUMINATED. AFTER PARKING AT THE GATE; I ENTERED 2 DISCREPANCY ITEMS IN ACFT MAINT LOGBOOK. ONE RPTING TCASII PROB. THE OTHER WARNING ELECTRONIC UNIT LIGHT ILLUMINATING FOR A SPLIT SECOND.