Ohm’s definition of resistance is given as $R=V/I$, so resistance is a ratio of the voltage and current. So the power of an Ohmic circuit
$$ P = VI = I^2R = \frac{V^2}{R} $$
and in case of alternating current, we have to average over time to get the power which, for sinusoidal currents, become
$$ \langle P\rangle = \langle I^2\rangle R = \frac{I_0^2R}{2} $$
because for sinusoidal currents, $\langle I^2\rangle = I_0^2/2$ which gives the definition of the radiation resistance of an antenna
$$ R \equiv \frac{2\langle P\rangle}{I_0^2} = \frac{2\pi^2}{3c} \left(\frac{l}{\lambda}\right)^2 $$
where the time-averaged power of a dipole antenna has been replaced by its full form.
The radiation resistance of free space can be found by using the definition of Poynting flux in Gaussian units:
$$ S = \frac{c}{4\pi} E^2 = \frac{cV^2}{4\pi l^2} = \frac{V^2}{R_0 l^2} $$
because $E=V/l$ and the impedance of free space
$$ R_0 = \frac{4\pi}{c} = \frac{1}{c\epsilon_0} = 377 \ \Omega $$
because $\epsilon_0=1/(4\pi)$ has to be used while converting from Gaussian to SI units. The definition of impedance of free space has to be this because $P=V^2/R$ which entails $S=V^2/(Rl^2)$ because flux is power per unit area.
A black hole has the same radiation resistance as free space because it is a perfect absorber. So a black hole totating in an external magnetic field can generate electricity with $V/I$ ratio of 377 $\Omega$ which might power the jets of a quasar.