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A giant planet can also remain inflated when power is deposited sufficiently deep to alter its internal energy budget. Candidate sources include tidal heating, Joule heating by wind-driven currents, and dissipation of circulation-driven mechanical energy. The depth and efficiency of deposition matter, as discussed in models of hot-Jupiter heating.

First construct the periodic response required in the introductory clause. At ${\omega }_0^2=1/(LC)$, the terms $L{I}_0^{\prime \prime }+I_0/C$ cancel for a sinusoid, leaving $R{I}_0^{\prime }={\omega }_0\cos ({\omega }_{0}t)$. ThusThis resonant series RLC response dissipates energy through Joule heating. Over one period,The Q factor, using the maximum magnetic energy $L{I}_M^2/2$, is consequently

Exoplanet transit photometry discovers a giant planet through a periodic flux decrement and measures $R_p/R_{\star }\simeq \sqrt{\delta }$. Stellar-radius estimates turn this into a planetary radius. The radial-velocity method discovers the stellar orbital reflex motion and constrains $M_p\sin i$. Follow-up exoplanet transit photometry is required to measure a geometric radius when such a planet also transits; a radial-velocity detection alone gives no direct size. Alternatively, exoplanet direct imaging finds young luminous giants, whose sizes are inferred less directly from luminosity, temperature, distance, and a planetary mass-radius relation or atmosphere model.

The two broad explanations for hot-Jupiter radius inflation are retention of primordial heat and addition of new interior power.

Delayed cooling of an inflated giant planet can arise from enhanced atmospheric opacity, which slows radiative escape; an irradiation-maintained radiative blanket, which insulates the convective interior; or compositional stratification and inefficient layered convection, which inhibit the outward transport of heat. These alter the rate of Kelvin-Helmholtz contraction.

Heating of an inflated giant planet can arise from tidal heating maintained by eccentricity or obliquity; Joule heating of currents driven by atmospheric winds through a magnetic field; or downward transport and dissipation of atmospheric mechanical energy generated by irradiation. To affect radius, the energy must be deposited at a depth and rate that changes the interior cooling balance. Simply absorbing starlight high in the atmosphere does not automatically supply deep heating. These are proposed mechanisms with different efficiencies, not six universally established contributions in every inflated planet.

For a resonator, the quality factor is $2\pi$ times the stored energy divided by the energy dissipated per cycle, using a specified steady-state stored-energy convention. A series RLC circuit at resonance has $Q=L{\omega }_0/R$, because its maximum magnetic energy is $L{I}_M^2/2$ and one cycle of Joule heating dissipates $\pi R{I}_M^2/{\omega }_0$.

An RLC circuit combines electrical resistance, inductance and capacitance. Stored energy can oscillate between magnetic and electric forms, while Joule heating dissipates it.