The paper discusses the problem of estimating the rotor time constant of the induction motor. Estimation is done considering that the stationary frame fluxes are available. The fluxes are obtained using a voltage model observer - the paper assumes that the stator resistance and the magnetizing inductance of the motor are known, therefore, the fluxes are accurate. The inverse of the rotor time constant is estimated with a MRAS-type sliding mode observer that uses the incoming fluxes to construct the feedback terms; it also uses a speed signal at the input. Since the speed may be inaccurate, this affects the estimation process. The paper shows that the error in the estimated rotor time constant can be reduced by operating the induction motor with a low ratio of id to iq. The estimation method involves only simple mathematics and is not computationally intensive. The theoretical claims of the paper are supported with simulations and experiments.