  Black hole jet power depends on the angular velocity of magnetic field lines,
$\Omega_F$. Force-free black hole magnetospheres typically have
$\Omega_F/\Omega_H \approx 0.5$, where $\Omega_H$ is the angular velocity of
the horizon. We give a streamlined proof of this result using an extension of
the classical black hole membrane paradigm. The proof is based on an
impedance-matching argument between membranes at the horizon and infinity. Then
we consider a general relativistic magnetohydrodynamic simulation of an
accreting, spinning black hole and jet. We find that the theory correctly
describes the simulation in the jet region. However, the field lines threading
the horizon near the equator have much smaller $\Omega_F/\Omega_H$ because the
force-free approximation breaks down in the accretion flow.
