The impedances of several electric double layer capacitors are analysed at high frequencies by using the Randles equivalent electric circuit with the semi-infinite Warburg impedance. The Warburg coefficient, the charge transfer resistance, the interfacial capacitance, as well as the geometric resistance of the devices are determined by means of a non-linear least squares fitting. Unlike other previous studies using this circuit, we identify the characteristic frequencies from the zero-pole representation at the limits of the Randles impedance at high and low frequencies. Our study includes the overlapping between the interfacial and porous transport processes in the equivalent series resistance at high frequencies and it additionally considers the frequency at the intersect point between the interfacial and porous regions in the impedance Nyquist plots. Evolution with time of the short-circuit current and the voltage drop in response to a current pulse in supercapacitors are theoretically analysed at the shortest times from numerical inversion of the Laplace transform by using PSpice(.). The numerical results obtained from the Randles impedance and those from the low-frequency Warburg approximation are compared, and the significance of the different time constants is analysed and discussed.