Using the methods of finite elements and conformal mappings the analytical models of the low resistance film resistors of the main types of comb (interdigital) structures with arbitrary relations of the specific resistances of resistive and conductive films have been built. In the resultant resistance the resistances of comb-like structure electrodes and connecting electrodes as well as additional resistance associated with the transmission of current from the conductive film to the resistive one and vice versa have been taken into account. The conditions, under which the boundary between the films can be considered as equipotential have been revealed. For this case the calculation has been performed by conformal mappings. The circuit of substitution of the low-impedance comb resistors, used as the current sensors in schemes of stabilization, control, thermal and current protection, has been constructed.