The ideal relative permittivity of liquid mixtures is demonstrated to be a volume-fraction-weighted average of the pure-component relative permittivities. This generalised-thermodynamics result is used to define the molar electric dipole, permittivity, dielectric polarization and electric susceptibility of thermodynamically ideal liquid mixtures and the corresponding excess properties. A hyperbolic approach is developed to the analysis of averaging formulae that are frequently used to predict the effective permittivity of composite materials. Some of these formulae are shown to be segments of rectangular hyperbolae with fixed asymptote values, whereas others can be understood in terms of rectangular hyperbolae with composition-dependent asymptote values. Relative permittivities of binary mixtures between tetraglyme and hexane, cyclohexane or benzene covering the complete composition range are reported at various temperatures. These data are used to outline a novel method for analysing the excess relative permittivity of liquid mixtures.