If I plan to measure the resistivity of a high resistivity material, would it not make sense to alter the geometry of the sensor to make A/l as small as possible and reduce the voltage to get a low resistance value to reduce the resistivity measured at conditions which are easy to fulfill experimentally. Because i'm a bit confused as i'm being told to increase the voltage and make sure A/l is large to measure the resistivity of this material. Thanks in advance for any help.
Best Answer
When you do the experiment typically you will apply some known voltage $V$ and measure the current $I$. This is given by:
$$ I = \frac{V}{R} = \frac{V}{\rho} \frac{A}{\ell} $$
Your problem is that if the resitivity, $\rho$, is very high then $V/\rho$ will be very small and the current $I$ will be too small to measure accurately. If so you can increase the current back to measurable levels by increasing the value of $A/\ell$.