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Electrical conductivity formulas are derived from first principles for fully ionized nonideal plasmas. The theory is applicable to an electron-ion system with a 1) Maxwell electron distribution with an arbitrary interaction parameter Â¿ = Ze2n1/3/KT (ratio of the mean coulomb interaction and thermal energies) and 2) Fermi electron distribution with an interaction parameter Â¿ = Ze2n1/3hÂ¿2m-1 n2/3 (ratio of the coulomb interaction and Fermi energies). The momentum relaxation time of the electrons in the plasma is calculated based on plane electron wave functions interacting with the continuum oscillations (plasma waves) through a shielded coulomb potential Us(r) = esee exp (-r/Â¿s)/r, which takes into account both electron-ion interactions (s = i) and electron-electron interactions (s = e). It is shown that the resulting conductivity formulas are applicable to higher densities, for which the ideal plasma conductivity theory breaks down because the Debye radius loses its physical meaning as a shielding length and upper impact parameter. The conductivity obtained for classical plasma is of the form Â¿c = Â¿c*(KT)3/2/m1/2e2 and agrees with the ideal plasma conductivity formula with respect to the temperature and density dependence for Â¿/Z Â¿ 0, but its magnitude is significantly reduced as Â¿/Z increases. For quantum plasmas, the conductivity obtained is of the form Â¿Q = Â¿Q*h3n/m2Ze2, which shows that the degenerate plasma behaves like a low-temperature metal.