  It has been pointed out in [1] that the familiar reciprocity relation between
the conductivity $\sigma$ and resistivity $\rho$ should not be expected to hold
in all possible settings, but, as argued in [2], is rather a property that may
(or may not) emerge as a consequence of specific features, or in certain limits
of interest, of a given theory. In this work, I prove the conventional
statement: $\rho= \sigma^{-1}$, which I refer to as $\textit{Ohm's reciprocity
relation}$, for a large class of holographic models with $d=3+1$ boundary
dimensions. The proof involves a generalisation of the electric-magnetic
duality in the $D=4+1$ bulk, the validity of which is discussed in detail. I
then confirm these findings by considering one specific model and run numerical
simulations in different settings.
