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Dual-band and broadband rectangular microstrip antennas are realized by cutting U slots, V slots, or a pair of rectangular slots inside the patch. In these designs, depending upon where the slot is cut, the slot length is taken to be equal to either a quarter-wavelength or a half-wavelength in length. However, these simpler approximations of slot length as a function of frequency do not give a close match for different slot lengths and their positions inside the patch. In this paper, the surface currents and voltage distributions for a dual-band pair of rectangular slots, and for U-slot-cut rectangular microstrip antennas, are studied over a wide frequency range. It was observed that the slot does not introduce any mode, but reduces the higher-order orthogonal mode resonance frequency of the patch and, along with the fundamental mode, realizes the dual-band response. Furthermore, by studying the current and voltage distributions, a formulation for the slot's resonant length on a glass epoxy substrate was proposed. The frequencies calculated using the proposed formulations agreed well with the simulated values, with an error of less than 5%. These formulations were also validated on RT-duroid substrate.