A turbocharger includes a compressor arrangement for compressing fresh air for internal combustion engines, containing a compressor wheel as well as an electric motor with a rotor and stator. A rotor magnet of the rotor is designed such that it is partially or completely integrated into the compressor wheel, and the smallest diameter of the stator is 1.5- to 8-times the size of the largest outer diameter of the rotor. The turbocharger has a very spontaneous response behaviour in the transient range, as well as the possibility of an exact real-time regulation of the mass flow. It furthermore renders possible the energy recovery and this contributes to increasing the total efficiency.