Also note that breakers do not trip immediately when their rating is exceeded. Residential (and light duty commercial) breakers have two independent trip mechanisms - thermal and magnetic. The thermal mechanism handles overloads has a “time to trip” curve - the breaker will trip if the load current stays above the rated current for a specified time. For example, NEMA requires that a 20A breaker trip within one hour for a 135% overload (27A) and within two minutes for a 200% overload (40A). The time to trip accounts for the fact that the branch circuit wiring protected by the breaker takes some time to heat to a damaging temperature.
The magnetic trip mechanism handles short circuits and is also called “instantaneous trip”. When the current (actually the change in current) exceeds a certain level the breaker trips instantly (in a few tens of milliseconds, anyway).
TL;DR - Circuit breakers do not trip instantly when they rated current is exceeded. Small overloads will take up to an hour to trip the breaker.