We introduce a novel apparatus designed for stress-controlled rheometers to perform simultaneous rheological and electrical measurements on strongly conductive complex fluids under shear. By means of a non-toxic liquid metal at room temperature, the electrical connection to the rotating shaft is completed with minimal additional mechanical friction, allowing for simultaneous stress measurements as low as 1 Pa. We use the capabilities of this design to perform an extensive set of rheo-electric experiments on gels formulated from attractive carbon black particles, at concentrations ranging from 4 to 15% wt. First, experiments on gels at rest prepared with different shear history show a robust power-law scaling between the elastic modulus G′₀ and the conductivity σ0 of the gels, i.e. G′₀ ∼ σ₀^α, with α=1.65 ± 0.04 independently of the gel concentration. Second, conductivity measurements performed simultaneously with creep experiments reveal for the first time that plastic events take place in the bulk while the shear rate decreases as a weak power law of time in the early stage of the experiment. The subsequent evolution of the conductivity and shear rate allows us to propose a local yielding scenario that is in agreement with previous velocimetry measurements. Finally, we determine the constitutive rheological and electrical behavior of carbon black gels. Corrections first introduced for mechanical measurements are carefully extended to electrical measurements to accurately distinguish between bulk and surface contributions to the conductivity. As an illustrative example, we examine the constitutive rheo-electric properties of five carbon black gels of different grades, and demonstrate the relevance of the novel rheo-electric apparatus as a versatile characterization tool for strongly conductive complex fluids and their applications.