We use low-density series expansions to calculate critical exponents for the behavior of random resistor networks near the percolation threshold as a function of the spatial dimension d. By using scaling relations, we obtain values of the conductivity exponent μ. For d=2 we find μ=1.43±0.02, and for d=3, μ=1.95±0.03, in excellent agreement with the experimental result of Abeles et al. Our results for high dimensionality agree well with the results of ε-expansion calculations.