  The Johnson-Nyquist noise in narrow wires having a transverse size smaller
than the screening length is shown to be white up to the frequency $D/L^2$ and
to decay at higher frequencies as $\omega^{-{1/2}}$. In two-dimensional films
having a thickness smaller than the screening length, the Johnson-Nyquist noise
is predicted to be frequency independent up to the frequency $\sigma_{2D}/L$
and to have a {\it universal} $1/\omega$ spectrum at higher frequencies. These
results are contrasted with the conventional noise spectra in neutral and
three-dimensional charged liquids.
