A lightning transmission device between the rotor and the nacelle in the wind turbine, configured to be installed in a wind turbine of blades turning with respect to a hub, where said wind turbine comprises additionally a gutter element, and the transmission device comprising: - a first electricity conductor platen, where one of its ends is separated at a distance from a metal strip placed at a root of each blade; - A second electricity conductor platen, where one of the ends is separated at a distance from the gutter element of said wind turbine; - electricity conductor means between the first and second platen; - an electrical insulator coupled to said first and second conductor platens, where said insulator is coupled also to the hub of said wind turbine; - relative displacement means between the first and second platen, characterized in that said relative displacement means configured to ensure a predefined distance between the end of the first platen and the metal strip located at the root of each blade; and between the end of the second platen and the gutter element;and said relative displacement means between both platens comprise: - an oblong groove belonging to the second platen, - at least a hole (1a, 1b) belonging to the first platen, which is located internally with respect to the projection of the oblong groove of the second platen on the first platen; and where at least a fixation is coupled respectively to the groove and the hole (1a, 1b), allowing to modify the relative position between the two platens (1, 2) based on the length of said groove. - a first elastic spring coupled on one side to the first platen, and on the other side to the insulator; - a second elastic spring coupled on one side to the second platen, and on the other side to the insulator; - an electrical conductor wire coupled both to the first platen and to the second platen, and - where in each end of each platen (1,2) closest to the metal strip and to the gutter element, respectively, two insulating elements (10, 11) are positioned, configured to contact in said metal strip and the gutter element, respectively, thanks to the elastic strength of both elastic springs (1d, 2d); and said insulating elements (10, 11) being configured to avoid contact between the ends of the platens (1, 2) and the metal strip and the gutter element, respectively. - a first electricity conductor platen, where one of its ends is separated at a distance from a metal strip placed at a root of each blade; - A second electricity conductor platen, where one of the ends is separated at a distance from the gutter element of said wind turbine; - electricity conductor means between the first and second platen; - an electrical insulator coupled to said first and second conductor platens, where said insulator is coupled also to the hub of said wind turbine; - relative displacement means between the first and second platen, characterized in that - an oblong groove belonging to the second platen, - at least a hole (1a, 1b) belonging to the first platen, which is located internally with respect to the projection of the oblong groove of the second platen on the first platen; and where at least a fixation is coupled respectively to the groove and the hole (1a, 1b), allowing to modify the relative position between the two platens (1, 2) based on the length of said groove. - a first elastic spring coupled on one side to the first platen, and on the other side to the insulator; - a second elastic spring coupled on one side to the second platen, and on the other side to the insulator; - an electrical conductor wire coupled both to the first platen and to the second platen, and - where in each end of each platen (1,2) closest to the metal strip and to the gutter element, respectively, two insulating elements (10, 11) are positioned, configured to contact in said metal strip and the gutter element, respectively, thanks to the elastic strength of both elastic springs (1d, 2d); and said insulating elements (10, 11) being configured to avoid contact between the ends of the platens (1, 2) and the metal strip and the gutter element, respectively.