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Experiments are performed to characterize the electrical properties of plasma filaments that are generated by self- guided femtosecond laser pulses propagating in air. A single plasma filament passes through a high-voltage sphere pulsed at -100 kV to a grounded electrode, which serves as a current monitor. The experiments utilize moderate electric fields to probe the filament conductivity, thereby avoiding the strong perturbations caused by electric discharges. The measured filament current decreases as ~1/R2 as the separation R between the electrodes is increased up to 1.5 m. The pulselength of the filament current signal is 2 ns (full-width at half-maximum), but the time resolution is limited by the bandwidth of the oscilloscope. The typical plasma density in the conducting filament is 9 times 1015 cm-3, which is inferred from the conductivity measurements and the size of the optical filaments. Comparisons are made with mobility values derived from electron swarm data, where the mobility depends upon the applied electric field. The conductivity of the filament is measured as the laser pulselength is varied from 50 fs to 1.5 ps. We find that relatively long laser pulses (1 ps) produce filaments with the largest conductivity. A model is used to predict the longitudinal position where the plasma filament forms and is in reasonably good agreement with measurements.