Forgot to add that if the battery has been sitting in the back at -5C for an hour or so in the cruise at 5000 feet or whatever then due to being cold soaked at low temperature the charge will be somewhat depleted.
Best answer to your friend's examiner would probably be "not very long"; but certainly long enough for a return to terra firma pronto to get it fixed. Either that or tell ATC what has happened, switch everything off, get out the map, compass and stopwatch and find an airfield that accepts no radio.
Smithy