In today's era, the widespread adoption of mobile terminals, particularly smartphones, has been facilitated by the rapid advancements in information and communication technology. However, a notable drawback of smartphones is their high-power consumption, necessitating faster charging solutions to enhance user convenience. This paper focuses on the RLC circuit of fast chargers. Initially, it introduces the fundamental principles and associated protocols of fast charging technology, elucidating the operation of integrated circuits within fast chargers and highlighting the advantages of fast charging compared to conventional slow charging methods. Moreover, the paper conducts an in-depth analysis of the transient processes within the pivotal series RLC circuit in fast chargers, encompassing zero-input responses and sinusoidal AC excitation responses. The transient processes are categorized into overdamped, critically damped, or underdamped states based on circuit element parameters, with initial conditions and power supply phase determining whether the circuit transitions directly into a steady-state process when stimulated by sinusoidal AC. This research contributes to a deeper understanding of the RLC circuit within smartphone fast chargers and serves as a valuable reference for advancing the development of fast charging solutions.