  We consider a Luttinger liquid (LL) connected to two reservoirs when the two
sample-reservoir interface resistances $R_{S}$ and $R_{D}$ are arbitrary (not
necessarily quantized at half-the-quantum of resistance). We compute exactly
the dynamical impedance of a Luttinger liquid and generalize earlier
expressions for its dynamical conductance in the following situations. (i) We
first consider a gated Luttinger liquid. It is shown that the Luttinger liquid
parameters $u$ and $K$ and the interface resistances $R_{S}$ and $% R_{D}$ can
be experimentally determined by measuring both the dynamical conductance and
impedance of a gated wire at second order in frequency. The parallel law
addition for the charge relaxation resistance $R_{q}$ is explicitly recovered
for these non-trivial interface resistances as $R_{q}^{-1} = R_{S}^{-1} +
R_{D}^{-1}$. (ii) We discuss the AC response when only one electrode is
connected to the LL. (iii) Thirdly we consider application of an arbitrary AC
electric field along the sample and compute the dynamical response of the LL
with arbitrary interface resistances. The discussion is then specialized to the
case of a uniform electric field.
