  Measuring large electrical resistances forms an essential part of common
applications such as insulation testing, but suffers from a fundamental
problem: the larger the resistance, the less sensitive a canonical ohmmeter is.
Here we develop a conceptually different electronic sensor by exploiting the
topological properties of non-Hermitian matrices, whose eigenvalues can show an
exponential sensitivity to perturbations. The ohmmeter is realized in an
multi-terminal, linear electric circuit with a non-Hermitian conductance
matrix, where the target resistance plays the role of the perturbation. We
inject multiple currents and measure a single voltage in order to directly
obtain the value of the resistance. The relative accuracy of the device
increases exponentially with the number of terminals, and for large resistances
outperforms a standard measurement by over an order of magnitude. Our work
paves the way towards leveraging non-Hermitian conductance matrices in
high-precision sensing.
