We present a black-box model of miniature circuit breakers having a realistic physical background. In compliance with basic physics, engineering know-how and magneto-hydrodynamics arc simulations, two sets of differential-algebraic equations are derived to model air plasma chemical dynamics and its interaction with breaker's physical environment (chamber shape, splitter plates, arc traveling). A numerically efficient and accurate electrical model at the breaker terminals is proposed. Its behaviour is shown by comparing simulations with short circuit experiments. Applications are at system level, including simulation of networks with several breakers, such as multiphase switching transients, selectivity and coordination with fuses, other breakers and surge protection devices.