The physical constraints on the scaling law of global energy confinement time have been derived based on a set of weakly relativistic collisional/collisionless Maxwell-Vlasov equations. A total of 106 L-mode electron cyclotron heating (ECH) data were selected from the T-10 and DIII-D tokamaks. These data, through statistical regression analysis, were processed to obtain the scaling law. The resultant scaling becomes if the collisional physical constraint is imposed. The scaling passed the statistical test and was found to describe the database well. Hence, the weakly relativistic collisional model is suggested to be adequate to depict the ECH mechanism.