  In the presence of a magnetic field and weakly ionizing winds, ohmic
dissipation is expected to take place in the envelopes of Jovian and lower-mass
planets alike. While the process has been investigated on the former, there
have been no studies done on mini-Neptunes so far. From structure and thermal
evolution models, we determine that the required energy deposition for halting
the contraction of mini-Neptunes increases with planetary mass and envelope
fraction. Scaled to the insolation power, the ohmic heating needed is small
$\sim10^{-5}$ -- orders of magnitude lower than for exo-Jupiters $\sim
10^{-2}$. Conversely, from solving the magnetic induction equation, we find
that ohmic energy is dissipated more readily for lower-mass planets and those
with larger envelope fractions. Combining these two trends, we find that ohmic
dissipation in hot mini-Neptunes is strong enough to inflate their radii ($\sim
10^{15}$ W for $T_{eq}=1400K$). The implication is that the radii of hot
mini-Neptunes may be attributed in part to ohmic heating. Thus, there is a
trade-off between ohmic dissipation and H/He content for hot mini-Neptunes,
adding a new degeneracy for the interpretation of the composition of such
planets. In addition, ohmic dissipation would make mini-Neptunes more
vulnerable to atmospheric evaporation.
