  We develop a characterization method of electroconvection structures in a
planar nematic liquid crystal layer by a study of the electric current
transport. Because the applied potential difference has a sinusoidal time
dependence, we define two electric Nusselt numbers corresponding to the
in-phase and out-of-phase components of the current. These Nusselt numbers are
predicted theoretically using a weakly nonlinear analysis of the standard
model. Our measurements of the electric current confirm that both numbers vary
linearly with the distance from onset until the occurence of secondary
instabilities; these instabilities also have a distinct Nusselt number
signature. A systematic comparison between our theoretical and experimental
results, using no adjusted parameters, demonstrates reasonable agreement. This
represents a quantitative test of the standard model completely independent
from traditional, optical techniques of studying electroconvection.
