We show that silicon nitride can provide uniform coverage of graphene in field-effect transistors while preserving the channel mobility. This insulator allowed us to study the maximum channel resistance at the Dirac (neutrality) point as a function of the strength of a perpendicular electric field in top-gated devices with different numbers of graphene layers. Using a simple model to account for surface potential variations (electron-hole puddles) near the Dirac point we estimate the field-induced band gap or band overlap in the different layers.