The problem of driving quasi-steady-state currents in tokamak plasmas with pulsed RF sources is examined in the regime , where τRF is the length of the RF pulse, is the electron collision time, TRF is the period between RF pulses, and TL/R is the L over R time of the tokamak plasma. This regime is appropriate to the proposed Microwave Tokamak Experiment (MTX) in which a pulsed free electron laser will be used to drive current in Alcator C. It is found that δI/Ī ≈ TRF/TL/R ≪ 1, where δI/Ī is the fractional variation in the plasma current. The production of runaway electrons can be a problem in the collisional limit, νe TRF ≫ 1. This will be avoided in the proposed MTX experiment if the electron temperature exceeds 1.5 keV.