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Switches based on high-temperature superconducting (HTS) thin films have been developed for the application in fault current limiters and various controlling devices. HTS thin film structures needed for this purpose have usually been fabricated as long multi-layered elements, in which HTS thin film is deposited on a dielectric substrate with high heat conductivity and covered by a thin layer with high electric conductivity. The main challenge has been to provide the fast and simultaneous transition of the whole of switch from the superconducting to the normal state. We experimentally investigated, under DC and AC conditions, the superconducting-normal state (S-N) transition in switches fabricated from parallel and series-connected YBCO thin films. The films were deposited on a sapphire substrate of 0.5 mm in thickness and covered by 100 nm Au layer. The appearance and propagation of normal zones in the films were determined by measuring the voltage drop across their different sections. The results were compared with ones obtained for a single film. The conditions providing a simultaneous S-N transition of the whole of the switch are discussed. It is shown that shunting the film by a resistor improves both the film protection from overheating and the homogeneity of S-N transition in the switch.