Integral expressions for the radiation resistances of a point source of electric current and a filament of finite length with a triangular current distribution are obtained for the case in which these sources are immersed in a loss-free and unbounded magnetoionic medium so that they are parallel to the direction of the magnetostatic field. The radiation resistance of the point source of electric current is found to become infinite in two frequency ranges, whose values are stated precisely, and this infinite behaviour is related to the medium resonances. It is found that, for the current filament, the radiation resistance remains finite for all frequencies except the upper hybrid resonant frequency. The reasons for the infinite behaviour of the radiation resistance at the upper hybrid resonant frequency are due to the limitations of the magnetoionic theory on which the present work is based. Numerical results for the radiation resistances of the two elementary electric-current sources are given for some typical values of the parameters of interest.