A lumped parameter model for tokamak plasma current and inductance time evolution as function of plasma resistance, non-inductive current drive sources and boundary voltage or Poloidal Field (PF) coil current drive is presented. Having in mind its application in a tokamak inductive control system, the model is expressed in state space form, the preferred choice for the design of control systems using modern control systems theory. The choice of system states allow many interesting physical quantities such as plasma current, inductance, magnetic energy, resistive and inductive fluxes etc be made available as output equations. The model is derived from energy conservation and flux balance theorems, together with a first order approximation for flux diffusion dynamics. The validity of this approximation has been checked using experimental data from JET showing an excellent agreement.