Originally posted by @Nathan Caron:
This is not an overload situation. It is standard practice to have a microwave on the same circuit as a gas range, especially when the microwave is mounted above the range. A 20 Amp breaker is sufficient for this circuit.
Unplug both appliances and reset the breaker. If it doesn't trip immediately, try pluging a lamp into one of the outlets and turning it on, if it still doesn't trip then you can be pretty confident the wiring is ok.
I would then check the breaker, as it is common to have afci breakers be overly sensitive. If you have experience working on electrical equipment you could swap the wires on the breaker in question with those on a breaker that is known to be good. If the circuit no longer trips, you know the breaker is the issue and can replace it. If the Circuit continues to trip with both appliances connected, unplug one and try again. This way you will be able to narrow down which appliance is the issue.
If you do not have experience working on electrical equipment, hire an electrician! 120v is more than enough to kill you. Your life and property have a much higher value than what you will pay for a service call.
I'm an electrician by the way ;)
Thanks. You're right on the oven being gas. It has been five days since the breaker tripped last time. Everything looks OK so far. I will fly you here if I need an electrician.
BTW, I live in Boston area, where is not too far away from you.