  The perfectly linear temperature dependence of the electrical resistivity
observed as $T \rightarrow$ 0 in a variety of metals close to a quantum
critical point is a major puzzle of condensed matter physics . Here we show
that $T$-linear resistivity as $T \rightarrow$ 0 is a generic property of
cuprates, associated with a universal scattering rate. We measured the
low-temperature resistivity of the bi-layer cuprate Bi2212 and found that it
exhibits a $T$-linear dependence with the same slope as in the single-layer
cuprates Bi2201, Nd-LSCO and LSCO, despite their very different Fermi surfaces
and structural, superconducting and magnetic properties. We then show that the
$T$-linear coefficient (per CuO$_2$ plane), $A_1$, is given by the universal
relation $A_1 T_F = h / 2e^2$, where $e$ is the electron charge, $h$ is the
Planck constant and $T_F$ is the Fermi temperature. This relation, obtained by
assuming that the scattering rate 1 / $\tau$ of charge carriers reaches the
Planckian limit whereby $\hbar / \tau = k_B T$, works not only for hole-doped
cuprates but also for electron-doped cuprates despite the different nature of
their quantum critical point and strength of their electron correlations.
