Is it possible to reliably determine the resistivity of a highly resistive liquid above the breakdown voltage (i.e. after ionising the substance)?
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You can determine the resistivity of anything, by measuring the voltage that causes a current to flow.
It's only useful to say that you've 'determined' the resistivity if it's reasonably linear (so stays the same as the voltage varies) and constant (is the same tomorrow as today).
The ionised fluid after a breakdown due to excessive voltage tends to have a conductivity that varies over many orders of magnitude, determined by the power that's being dissipated in it, the output impedance of the power source, and any impurities in it. It is very, very non-constant, and non-linear. Any breakdown may release material from the electrodes, changing the impurity level.
Neil_UK
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