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We revisit the problem of the dynamic response of a superconducting bridgeafter abruptly switching on the supercritical current $I>I_c$. In contrast toprevious theoretical works we take into account spatial gradients and use boththe local temperature approach and the kinetic equation for the distributionfunction of quasiparticles. In both models the finite delay time $t_d$ in thevoltage response is connected with temporary cooling of quasiparticles due tothe suppression of the superconducitng order parameter by current. We find that$t_d$ has different values and different temperature dependencies in theconsidered models. In turns out that the presence of even small inhomogeneitiesin the bridge or of bulk leads/contacts at the ends of the {\it homogenous}bridge favors a local suppression of the superconducting order parameter$|\Delta|$ during the dynamic response. It results in a decrease of the delaytime, in comparison with the spatially uniform model, due to the diffusion ofnonequilibrium quasiparticles from the region with locally suppressed$|\Delta|$. In case the current distribution is spatially nonuniform across thebridge the delay time is mainly connected with the time needed for thenucleation of the first vortex at the position where the current density ismaximal (at $I\sim I_c$ and for not very wide films). We also find that a shortalternating current pulse (sinusoid like) with zero time-average may result ina nonzero time-averaged voltage response where its sign depends on the phase ofthe ac current.

Temporary cooling of quasiparticles and delay in voltage response of superconducting bridges after abrupt switching on the supercritical current