Radiation resistance ($P_{\mathrm{rad}}=I_{\mathrm{rms}}^2{R}_{\mathrm{rad}}$)

Radiation resistance represents emitted electromagnetic power as a real input resistance of an antenna. It does not describe conversion to heat inside the conductor. If peak current amplitude is used, $P_{\mathrm{rad}}=|I_0{|}^2{R}_{\mathrm{rad}}/2$. Real ohmic loss adds a separate resistance and lowers radiation efficiency. For an ideal short uniform-current element of length $d$, the Hertzian dipole gives $R_{\mathrm{rad}}=80{\pi }^2(d/\lambda {)}^2$ in ohms, using the usual vacuum impedance approximation $120\pi \Omega$.

A fixed electrically small loop of area A with peak sinusoidal current $I_0\cos \omega t$ has magnetic moment $m=AI$. The magnetic dipole radiation law gives mean power ${\mu }_0{A}^2{I}_0^2{\omega }^4/(12\pi c^3)$. Defining it as $I_0^2{R}_{\mathrm{rad}}/2$ yields $R_{\mathrm{rad}}={\mu }_0{A}^2{\omega }^4/(6\pi c^3)$. This equivalent resistance accounts for radiation, not heating in the conductor. Rotating the loop changes its vector moment and cannot in general be modelled by the same scalar current alone.