In an alternating current generator, a rotor is provided radially inside a stator core. A rotor core has a cylindrical boss press-fit around a rotor shaft, disc portions extending from an outer periphery of the boss in a radial direction, and claw pieces in connecting with the disc portions radially outside the boss. A field winding is provided between the boss and claw pieces. An annular core is provided on an outer periphery of the claw pieces. The annular core is made of a stack of core sheets and has slits formed in the radial direction. Iron loss is decreased and leaks of magnetic fluxes in the annular core are suppressed by the slits.