Several issues to be aware of.  The circuit breaker may be bad and not tripping under too high a load, or the circuit breaker may be a higher amperage than the outlet and load calls for.

The safest way to tell which breaker it is without touching anything is to get a touchless voltage sensor (about $6 to $10 at Radio Shack, Home Depot, and etc.) and check the outlet for power as you turn off the breakers one by one.  If the outlet functions well enough to plug a radio into, turn the radio on loud and when you get to the right breaker the radio will turn off.

Also, you now have to find out what is wrong with what you plugged in when the fire started.