The resistivity response equation of sandstone is the most important basis for well logging interpretation to determine the water saturation of reservoir, but the Archie formula and its derivations are all empirical formulas, and the test error by experimental data is more than 20%. Because the coincidence rate of the log interpretation of low resistivity oil layers and high resistivity water layers is low in the current, In order to further improve the calculation accuracy of reservoir water saturation, it is particularly necessary to deeply understand the essence of rock conductivity. Based on the main influencing factors of rock conductivity, It is considered that for rocks with given formation water resistivity and porosity, the influence of pore structure, size, argillaceous content and conductive minerals on rock conductivity is constant and is an inherent factor. rock resistivity only changes with the change of connected pore water volume, Therefore, the establishment of the relationship between rock resistivity and connected pore water volume conforms to the functional relationship form of dependent variable and independent variable, and can reflect the nature of the rock-electricity relationship. On this basis, the model of rock conductivity per unit volume is proposed, the response equation of sandstone resistivity is deduced, and the general form of the response equation of sandstone resistivity is obtained. The results show that the formula is in good agreement with the experimental data, with a correlation coefficient of more than 0.99, and the test error of the experimental data is no more than 5%, which can represent the theoretical form of the rock resistivity response equation. The new formula considers that rock resistivity and connected pore water volume or water saturation are power functions, which solves some obscure problems in rock resistivity response equation for many years. The parameters of the formula are the inherent property parameters of rocks, which have certain value in use. Based on the new formula, the formula of calculating the water saturation of a reservoir by using the ratio of radial resistivity has been obtained in practical application to some extent. it shows that the new formula is not only of theoretical significance, but also of practical application significance, and is worth further popularizing.