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We revisit a classical problem of theoretical electrochemistry: the responseof an electric double layer capacitor (EDLC) subject to a small, suddenlyapplied external potential. We solve the Debye-Falkenhagen equation to obtainexact expressions for key EDLC quantities: the ionic charge density, the ioniccurrent density, and the electric field. In contrast to earlier works, ourresults are not restricted to the long-time asymptotics of those quantities.The solutions take the form of infinite sums whose successive terms all decayexponentially with increasingly short relaxation times. Importantly, this setof relaxation times is the same among all aforementioned EDLC quantities; thisproperty is demanded on physical grounds but not generally achieved withinapproximation schemes. The scaling of the largest relaxation timescale$\tau_{1}$, that determines the long-time decay, is in accordance with earlierresults: depending on the Debye length, $\lambda_{D}$, and the electrodeseparation, $2L$, it amounts to $\tau_{1}\simeq\lambda_{D} L/D$ for$L\gg\lambda_{D}$, and $\tau_{1} \simeq 4 L^2/(\pi^2 D)$ for $L\ll\lambda_{D}$,respectively (with $D$ being the ionic diffusivity).

Transient dynamics of electric double-layer capacitors: Exact expressions within the Debye-Falkenhagen approximation