= Hall resistance
{title2=$R_{xy}$}
{title2=$R_H$}
In some contexts, we want to observe what happens for a given fixed <magnetic field> strength on a specific plate (thus $t$ and $n$ are also fixed).
In those cases, it can be useful to talk about the "Hall resistance" defined as:
$$
R_{xy} = \frac{V_y}{I_x}
$$
So note that it is not a "regular resistance", it just has the same dimensions, and is more usefully understood as a proportionality constant for the voltage given an input $I_x$ current:
$$
V_y = R_{xy} I_x
$$
This notion can be useful because everything else being equal, if we increase the current $I_x$, then $V_y$ also increases proportionally, making this a way to talk about the voltage in a current independent manner.
And this is particularly the case for the <quantum Hall effect>, where $R_{xy}$ is constant for wide ranges of applied <magnetic field> and TODO presumably the height $t$ can be made to a single molecular layer with <chemical vapor deposition> of the like, and if therefore fixed.