We present analytical results on the transient current response of noninteracting open electronic systems under time-dependent external voltages in both linear- and nonlinear-response regimes. The derivations are based on an equation of motion formalism for the system reduced single-electron density matrix (Zheng et al 2007 Phys. Rev. B 75 195127). Dissipative interactions between the system and leads are treated by the nonequilibrium Green's function approach. The linear-response dynamics is characterized by the analytical admittance spectrum of the open system, through which the quantum coherent transport properties are mapped to equivalent classical circuits. The nonlinear-response current spectrum not only resolves the intrinsic energetic configuration of the system, but also reflects the unique dynamical features due to the transient characteristics of the applied voltages.