In this paper, a database of L-mode plasmas with Greenwald density fractions smaller than 0.8 is used to analyse the parametric dependences of the radiative power and the effective charge Zeff. It is found that the radiative power has a linear dependence on the total power and a linear fit is derived.In order to understand this parametric dependence, the changes in the radial extension of the radiation are studied with the help of bolometry measurements and it is found that the increase in Prad with Ptot can be explained by an increase in the neutral source of impurities (basically carbon erosion) during additional heating. A comparison of deuterium and helium plasmas shows that they radiate the same amount at the same total power. Significant positive deviations from the fit of the radiative power are observed for high ratios of Cu XIX/⟨ne⟩. Zeff is also found to depend roughly linearly on the total power. The link found between Zeff and Prad is compatible with that of multimachine scaling (Matthews et al 1997 J. Nucl. Mater.241–243 450). These results are obtained in a limiter machine, running in L-mode in the case where carbon is the dominant impurity.