One-piece voltage regulator/brush-holder assembly for a rotary electrical machine and rotary electrical machine including such an assembly

An electrical machine such as an alternator or starter-alternator for a motor vehicle which is fitted with the one-piece voltage-regulator/brush-holder assembly (1). The brush-holder (6) is capable of guiding at least first and second brushes by means of respective first and second longitudinal recesses (7). The recesses are substantially parallelepiped, made of an electrically insulating material and extend substantially in an axial plane of a rotor of the machine. Each recess is provided with at least one respective longitudinal internal groove (9) in communication with at least one channel (11) provided in a body (6) of the assembly (1), in an axial direction (XX′) of the rotor, and intended for a coolant (8) to pass therethrough. A first cross section of the first internal groove is between 5% and 7% of a second cross section of the recesses.