  We present the first three-dimensional circulation models for extrasolar gas
giant atmospheres with geometrically and energetically consistent treatments of
magnetic drag and ohmic dissipation. Atmospheric resistivities are continuously
updated and calculated directly from the flow structure, strongly coupling the
magnetic effects with the circulation pattern. We model the hot Jupiters HD
189733b (Teq \approx 1200 K) and HD 209458b (Teq \approx 1500 K) and test
planetary magnetic field strengths from 0 to 30 G. We find that even at B = 3 G
the atmospheric structure and circulation of HD 209458b are strongly influenced
by magnetic effects, while the cooler HD 189733b remains largely unaffected,
even in the case of B = 30 G and super-solar metallicities. Our models of HD
209458b indicate that magnetic effects can substantially slow down atmospheric
winds, change circulation and temperature patterns, and alter observable
properties. These models establish that longitudinal and latitudinal hot spot
offsets, day-night flux contrasts, and planetary radius inflation are
interrelated diagnostics of the magnetic induction process occurring in the
atmospheres of hot Jupiters and other similarly forced exoplanets. Most of the
ohmic heating occurs high in the atmosphere and on the day side of the planet,
while the heating at depth is strongly dependent on the internal heat flux
assumed for the planet, with more heating when the deep atmosphere is hot. We
compare the ohmic power at depth in our models, and estimates of the ohmic
dissipation in the bulk interior (from general scaling laws), to evolutionary
models that constrain the amount of heating necessary to explain the inflated
radius of HD 209458b. Our results suggest that deep ohmic heating can
successfully inflate the radius of HD 209458b for planetary magnetic field
strengths of B \geq 3 - 10 G.
