  We use both Eilenberger-Usadel and Ginzburg-Landau (GL) theory to calculate
the superfluid's temperature-dependent kinetic inductance for all currents up
to the depairing current in thin and narrow superconducting films. The
calculations apply to BCS weak-coupling superconductors with isotropic gaps and
transport mean-free paths much less than the BCS coherence length. The kinetic
inductance is calculated for the response to a small alternating current when
the film is carrying a dc bias current. In the slow-experiment/fast-relaxation
limit, in which the superconducting order parameter quasistatically follows the
time-dependent current, the kinetic inductance diverges as the bias current
approaches the depairing value. However, in the
fast-experiment/slow-relaxiation limit, in which the the superconducting order
parameter remains fixed at a value corresponding to the dc bias current, the
kinetic inductance rises to a finite value at the depairing current. We then
use time-dependent GL theory to calculate the kinetic impedance of the
superfluid, which includes not only the kinetic reactance but also the kinetic
resistance of the superfluid arising from dissipation due to order-parameter
relaxation. The kinetic resistance is largest for angular frequencies $\omega$
obeying $\omega \tau_s > 1$, where $\tau_s$ is the order-parameter relaxation
time, and for bias currents close to the depairing current. We also include the
normal fluid's contribution to dissipation in deriving an expression for the
total kinetic impedance. The Appendices contain many details about the
temperature-dependent behavior of superconductors carrying current up to the
depairing value.
