This study attempts to give some answers on how the electrical signal is impacted by conduit formation in limestone due to calcite dissolution, and how the electrical properties can be related to evolving structural parameters. Ensuring sustainable strategies to manage water resources in karst reservoirs requires a better understanding of the mechanisms responsible for dissolution features in the rock mass. The dissolution of carbonate core samples caused by CO2 or acid solution injection has already been well studied in the laboratory to understand the formation of conduits and their intricate coupling with transport properties such as permeability and porosity. However, these experiments generally rely on image analysis, an accurate technique that cannot be used in the field. Additionally, in a subsurface context, chemical analysis of the pore water can be quite intrusive, providing only restricted and spatially limited information. Thus, studying large-scale heterogeneities such as karst environments can benefit from the use of non-invasive tools such as the ones proposed in hydrogeophysics. In particular, geoelectrical methods are good candidates to detect the emergence of karstification related to the heterogeneous dissolution of large volumes since they present a high sensitivity to the physical and chemical properties of both porous matrix and interstitial fluids. We monitored the electrical conductivity, porosity, and permeability of two limestone core samples during controlled dissolution experiments driven by acid injection at atmospheric conditions under different flow rates creating preferential conduits. These two samples were also characterized before and after the acid percolation with laboratory methods and CT scan imaging. First, we confront the electrical conductivity variations to the evolution of permeability with time. We show that monitoring electrical properties allows us to sense the impact of dissolution in the porous medium long before the sample is percolated. This result is a key finding to highlight the great interest that electrical properties can represent in monitoring reactive percolation in karst systems. Then, we interpret the monitored electrical conductivity of the acid percolation with a physics-based model. This model describes the porous medium as a fractal cumulative distribution of tortuous capillaries with a sinusoidal variation of their radius. According to the model description, the sample electrical conductivity is interpreted in terms of effective structural parameters which are tortuosity and constrictivity. Confronting the model with the experimental results shows that the electrical signature of calcite dissolution is more impacted by the evolution of constrictivity than by tortuosity, while most of the literature focuses on the tortuosity and even neglects constrictivity when describing the pore space complexity with electrical conductivity measurements. Finally, based on our experimental results and data sets from the literature, we show that the characteristic Johnson length is a valuable structural witness of calcite dissolution impact linking electrical and hydrological properties. This small-scale approach to heterogeneous dissolution is an analog of the natural processes involved in forming conduits by dissolution leading to karstification. The results of this study are transferable to large-scale applications such as the survey of karst formation, CO2 geological storage, and geothermal energy recovery.