  Using semi-analytical, one-dimensional models, we elucidate the influence of
scattering and absorption on the degree of Ohmic dissipation in hot Jovian
atmospheres. With the assumption of Saha equilibrium, the variation in
temperature is the main driver of the variations in the electrical
conductivity, induced current and Ohmic power dissipated. Atmospheres
possessing temperature inversions tend to dissipate most of the Ohmic power
superficially, at high altitudes, whereas those without temperature inversions
are capable of greater dissipation deeper down. Scattering in the optical range
of wavelengths tends to cool the lower atmosphere, thus reducing the degree of
dissipation at depth. Purely absorbing cloud decks (in the infrared), of a
finite extent in height, allow for localized reductions in dissipation and may
reverse a temperature inversion if they are dense and thick enough, thus
greatly enhancing the dissipation at depth. If Ohmic dissipation is the
mechanism for inflating hot Jupiters, then variations in the atmospheric
opacity (which may be interpreted as arising from variations in metallicity and
cloud/haze properties) and magnetic field strength naturally produce a scatter
in the measured radii at a given strength of irradiation. Future work will
determine if these effects are dominant over evolutionary effects, which also
contribute a scatter to the measured radii.
