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Conventional circuit breakers suffer from two main deficiencies: they are slow to operate and develop an electrical arc. These may be overcome by using solid-state switches which in turn introduce other problems, most significantly power dissipated while in the on-state. Nevertheless, a number of solid-state devices are candidates for implementation as low-voltage circuit breakers and there are several options based on the semiconductor material that may function as high-power switches. This paper presents a unique, extensive and systematic evaluation of these options. Voltage-controlled devices are selected due to the simplicity of the controlling circuit and their resilience to $dv$/$dt$-induced switching. Properties of fully solid-state circuit breakers are established and systematic comparisons are made among switches built of silicon and other wide bandgap (WBG) devices such as SiC MOS and GaN HEMT transistors. Using SPICE simulation it is shown that solid-state circuit breakers (SSCBs) based on WBG devices exhibit superior characteristics compared with silicon devices, with faster switching and higher voltage and current ratings. Hybrid circuit breakers, combining both conventional and solid-state switches, are discussed too and a new design circuit is simulated and compared to both conventional and fully solid-state designs.