Current in a vacuum and resistance of metals

In a vacuum (a medium so rarefied that molecules do not collide) there are no charge carriers, so no current flows even when a voltage is applied between electrodes. To create carriers the cathode is heated: the emission of electrons from a hot metal is thermionic emission. Electrons leaving the cathode are accelerated by the anode (the positive electrode) and reach it – in a vacuum the current is the ordered motion of electrons. If the anode is negative and the cathode positive, the electrons return to the cathode and there is no current; thus a vacuum diode (a two-electrode tube with an anode and cathode) conducts in one direction. Its characteristic is not linear: at small voltages, because of the electron cloud near the cathode, the current grows as Iₐ ∝ U^(3/2) (the Boguslavsky–Langmuir three-halves law); when all electrons leaving the cathode reach the anode the current stops growing – the saturation current. The hotter the cathode the greater the saturation current. An electron accelerated through U gains energy eU = mυ²/2. Vacuum diodes were used to rectify alternating current before semiconductor diodes.