In this talk, we analyze Maxwell’s equations coupled with a generalized Ohm’s law in magnetohydrodynamics (MHD), a model used for wave propagation in plasmas and conducting media. In many plasma applications, magnetic fields and charged-particle dynamics introduce additional effects, such as Hall currents, ion-slip contributions, and inertial effects in the evolution of the current. These effects cannot be captured by the simple Ohm's law, and a generalized Ohm’s law is needed to represent the induced currents more accurately. We study both deterministic and random versions of the model, where uncertainty is introduced through the relaxation-time parameter. The deterministic system is discretized by a finite difference time domain (FDTD) method on a staggered Yee grid, and the random system is treated using a polynomial chaos expansion. We present results on stability, convergence, and dispersion, and we discuss their implications for accuracy and reliability of the numerical schemes.