We consider a square network formed of random electric resistances to the percolation threshold of bond Pc=0.5. We calculate the distribution of current on the infinite cluster with a constant current and constant tension, using a method of gradient conjugated accelerated by LU decomposition. Then we study the multifractal spectrum of the current distribution. Our numerical results are in agreement with the results in literature. The form of the distribution function is nearly Gaussian with the existence of a long tail in the weak current zone. This study leads us to the following findings: the insufficiency of the multifractality to describe all scales of currents; the distribution of strong currents is well understood and it is multifractal, meanwhile the weak currents stays imperfectly known.We also obtain a part of the spectrum which describes the very weak currents that we assign to the currents scales.