Models are developed for the semiconductor integrated-circuit resistor that account for changes in resistance resulting from changes in charge depleted from the resistor channel. The models therefore are applicable both to diffused resistors, in which this effect often may be neglected, and to expitaxially-grown resistors, where it may be an important factor. Because the models are derived systematically from physical make-up, element values are explicit functions of structural constants and of material parameters, such as mobility, dielectric constant and impurity concentration. This property links the steady-state and transient performance of the resistor as a circuit element with its physical construction and with the properties of its constituent materials. The practical utility of the models is demonstrated by employing them in calculating the switching time of an integrated inverter circuit. For small logic swings, the complete model, which includes both nonlinear resistance and capacitance, reduces to a model comprising only linear elements; for larger swings, the general nonlinear model must be used. In both cases, however, the switching time is formulated explicitly in terms of the structural and material constants of the resistor.